Induction step : Let the statement is true. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Sum of odd numbers always gives a perfect square. Asked 6 years, 3 months ago.
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The sum of all the odd numbers from zero to 16 is an even number. True or false?
We will consider the first odd number to be 3, not 1. I currently use a method which works well for small values of n, but would be very inefficient for large ones. Here's my method.Can you solve this mind blowing math puzzle? - Minute Math
Since I can only really add 1 number each time I advance, this algorithm will not be efficient for large n. Is there a better way? It does have some drawbacks, though. In addition to being very inefficient for large numbers, it also does not find all the possible answers for a given "n"; it always finds a single answer.
There are at least a couple of ways of attacking your problem which are more efficient and which if used properly find all the answers for a given "n".
Below are descriptions of two such methods, along with several examples. Method 1: using the idea of the sum of an arithmetic series Any time you have a sum of consecutive odd integers, you have an arithmetic series--a sum of a sequence of numbers in which the difference between successive elements is constant. In this case, the sum of the series of consecutive odd numbers is then the product of two odd numbers.
So in this case, the sum of the series of consecutive odd numbers is the product of two even numbers. The preceding analysis tells us that, whenever we can express an integer n as the product either of two odd integers or of two even integers, then we can find a sequence of consecutive odd integers whose sum is n and in which the number of elements is one of the two factors.
So the numbers are 9, 11, and The numbers are -7, -5, -3, -1, 1, 3, 5, 7, 9, 11, and In this sum, the negative numbers "cancel out" the positive odd integers through 7, leaving the other solution consisting of 9, 11, and But apparently you aren't considering negative integers in your problem, so I won't consider solutions involving negative integers from here on.
Note your algorithm finds the second of these solutions, because it starts with a smaller number. I will show this method for the other examples I worked with the preceding method So again we find 42 cannot be written as the sum of consecutive odd integers.
I hope at least some of this helps, and that it is not too much for you to digest.Some related Topics in Quantitative aptitude. The Concepts of number system the mathematics. Divisibility Rules of numbers from 1 to 20 Basic math education.
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Harmonic mean formula In this logarithm tutorial explained about logarithm applications with examples and solutions based the logarithmic formulas as per Your email address will not be published. Save my name, email, and website in this browser for the next time I comment. Formulas with examples for Sum of n Consecutive numbers Contents 1 Formulas with examples for Sum of n Consecutive numbers 1.
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Unanswered Questions. Math and Arithmetic. Wiki User Any numbers that cannot be divided by 2 is an odd number. The odd numbers from 1 to are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, Related Questions Asked in Math and Arithmetic What is the sum from all the odd numbers from 1 to ?
The sum of all the odd numbers from 1 through is 10, Asked in Math and Arithmetic The sum of the first positive odd numbers? The sum of the first odd numbers 1 through is ten thou. Since odd numbers are in a ratio of it means for every one odd there will be one even, there would be 50 odd numbers betweenand 50 even numbers. Look for a table of prime numbers. All the odd numbers that are NOT on this list are composite numbers. Asked in Math and Arithmetic What numbers between contain only odd digits?
All the odd numbers of the odd tens plus the odd numbers less than If the "between" excludes 1 andthen there are 29 such numbers.
What is the Sum of First 40 Odd Numbers?
Asked in Math and Arithmetic What is the sum of all odd numbers 1 through 99? The sum of all odd numbers 1 through 99 is 9, Asked in Math and Arithmetic, Gwalior Write a program which will display the list of even and odd numbers?
In Java: System.The concept of consecutive numbers may seem straightforward, but if you search the internet, you'll find slightly differing views about what this term means. Algebra problems often ask about properties of consecutive odd or even numbers, or consecutive numbers that increase by multiples of three, such as 3, 6, 9, Learning about consecutive numbers, then, is a bit trickier than is at first apparent.
Yet it is an important concept to understand in math, particularly in algebra. The numbers 3, 6, 9 are not consecutive numbers, but they are consecutive multiples of 3, which means that the numbers are adjacent integers. A problem may ask about consecutive even numbers—2, 4, 6, 8, 10—or consecutive odd numbers—13, 15, 17—where you take one even number and then the very next even number after that or one odd number and the very next odd number.
To represent consecutive numbers algebraically, let one of the numbers be x. If the question calls for consecutive even numbers, you would have to ensure that the first number you choose is even.
You can do this by letting the first number be 2x instead of x. Take care when selecting the next consecutive even number, though. Suppose the sum of two consecutive numbers is What are the numbers? Suppose you had chosen your consecutive numbers differently from the start.
In that case, let the first number be x - 3, and the second number be x - 4. These numbers are still consecutive numbers: one comes directly after the other, as follows:. To clear up this seeming discrepancy, substitute 10 for x, as follows:. For example, if you had a problem involving the product of five consecutive numbers, you could calculate it using either of the following two methods:.
Try these consecutive number problems. Even if you can figure out some of them without the methods discussed previously, try them using consecutive variables for practice:. Share Flipboard Email. Deb Russell. Math Expert. Deb Russell is a school principal and teacher with over 25 years of experience teaching mathematics at all levels.
So, your numbers are 6 and 7. You then have the same answer as in the previous problem. Four consecutive even numbers have a sum of Five consecutive numbers have a sum of zero. Two consecutive odd numbers have a product of Three consecutive multiples of five have a sum of The product of two consecutive numbers is If the sum of four consecutive integers is 46, what are the numbers?
The sum of five consecutive even integers is If you subtract the sum of two consecutive numbers from the product of the same two numbers, the answer is 5.
Do there exist two consecutive odd numbers with a product of 52? Do there exist seven consecutive integers with a sum of ? Setting up equations and solving leads to a non-integer solution for x.All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply.
Hottest Questions. Previously Viewed. Unanswered Questions. Math and Arithmetic. What is the sum of all odd numbers from 1 to ? Wiki User The sum of all odd numbers 1 tois 14, Asked in Math and Arithmetic What is the sum of all odd numbers from 1 to ? The sum of all the odd numbers between 1 and is Asked in Math and Arithmetic What is the sum from all the odd numbers from 1 to ?
The sum of all the odd numbers from 1 through is 10, Asked in Math and Arithmetic, Numbers What is the sum of all odd numbers from 1to 64? The sum of all odd numbers from 1 to 64 inclusive is 4, Asked in Math and Arithmetic What is the sum of all the odd numbers up to ?
The sum of the first odd numbers isAsked in Math and Arithmetic Is sum of odd numbers always even? The sum of two odd numbers is always even; the sum of three odd numbers is always odd; the sum of four odd numbers is always even; the sum of five odd numbers is always odd; etc. Asked in Math and Arithmetic What is the sum of all odd numbers 1 through 99?
The sum of all odd numbers 1 through 99 is 9, Asked in Math and Arithmetic, Numbers From zero to 16 is all the odd numbers the sum of even numbers? If this question means "in the interval 0 to 16 inclusive, is the sum of the odd numbers the same as the sum of the even numbers? The sum of the even numbers is eight more than the sum of the odd ones. You cannot. The sum of 5 odd numbers must be odd. Asked in Math and Arithmetic, Numbers What are the nine odd numbers whose sum is ?
The sum of an odd number of odd numbers will be odd. Asked in Math and Arithmetic Will the sum of 3 odd numbers be even? No, the sum of three odd numbers will always be odd.
Asked in Math and Arithmetic Five odd numbers whose sum is 20? That can't be solved. The sum of five odd numbers will always be an odd number. Asked in Math and Arithmetic Can you tell if sum of several numbers will be even or odd? Yes, all you have to do is to count the number of ODD numbers in the list. If it is odd, then the sum will be odd; if even, so will the sum. Knowing this can help you run a quick validity check when you sum up a list of numbers.Shortcut Tricks are very important things in competitive exam.
Time is the main factor in competitive exams. If you know how to manage time then you will surely do great in your exam. Most of us miss that part. We provide examples on Sum of all odd numbers starting from 1 shortcut tricks here in this page below.
We try to provide all types of shortcut tricks on sum of all odd numbers starting from 1 here. Visitors are requested to carefully read all shortcut examples. These examples will help you to understand shortcut tricks on Sum of all odd numbers starting from 1.
Before doing anything we recommend you to do a math practice set. Write down twenty math problems related to this topic on a page.
Do first ten maths using basic formula of this math topic. You also need to keep track of timing. Write down the time taken by you to solve those questions. Now go through our page for sum of all odd numbers starting from 1 shortcut trick. After finishing this do remaining questions using Sum of all odd numbers starting from 1 shortcut tricks. Again keep track of timing. You will surely see the improvement in your timing this time.
But this is not enough.
C program to find sum of odd numbers from 1 to n
You need more practice to improve your timing more. Math section in a competitive exam is the most important part of the exam. You can get a good score only if you get a good score in math section.
And, you can get good score only by practicing more and more. You should do your math problems within time with correctness, and only shortcut tricks can give you that success. You may do math problems within time without using any shortcut tricks. You may have that potential. Here we prepared all odd numbers sum starting from 1 shortcut tricks for those people. Here in this page we try to put all types of shortcut tricks on Sum of all odd numbers starting from 1.
But we may miss few of them. If you know anything else rather than this please do share with us. Your little help will help so many needy. In Addition numbers shortcut tricks we learned how to find the sum of consecutive number in a group following each other continuously. Now we learn how to find the sum of all odd numbers starting from 1 to using short cut tricks. This is the sum of all odd number present in 1 to series numbers, we know that in 1 to series number have fifty even and fifty will be odd number so we can do only half odd numbers.
We provide few tricks on Addition. Please visit this page to get updates on more Math Shortcut Tricks. You can also like our facebook page to get updates. If you have any question regarding this topic then please do comment on below section. You can also send us message on facebook. Sum of all odd numbers starting from 1 Shortcut Tricks are very important things in competitive exam. How to Solve Count the total odd numbers exists in between 1 to