find the sum of odd natural numbers upto 100
Answers
Answer:
this will may help you in your ans
Answer:
The very first thing , find the sum of all the consecutive integers,here you have 100 terms, so by using the sum of nterms of a series = n(n+1)/2. So here( 100 ×101 )/2 = 5050, then if you know exactly how many numbers between 1 to 100 are even numbers , find the even numbers and count like 2, 4, 6, 8, …….100 , here you will have exactly 50 numbers so by using the sum of n even numbers is n(n+1) so
50 (50+1)= 2550.then use the formula
Sum of odd consecutive integers from 1 to 100 = (Sum of all consecutive integers from 1 to 100) - (Sum of even consecutive integers from 1 to 100). Sum of odds = (100 x 101/2) - [ (50 x 51)] = 5050 - 2550 = 2500.
Another method
You can add a series of consecutive odd numbers manually, but there is a much easier way to do it, especially if you are dealing with a lot of numbers. Once you master a simple formula, you will be able to add these numbers in no time without the use of a calculator. There is also a simple way to find out which consecutive numbers add up to a given sum.
Choose an ending point. Before you get started, you need to determine what the last consecutive odd number in your set, This formula can help you add any number of consecutive odd numbers starting with 1. Here your ending point is 99.
Add 1. The next step is to simply add 1 to your ending point. You should now have an even number, which is essential for the next step. So here 99 +1 , which is a even number.
Divide by 2. Once you have an even number, you should divide this by 2. This will give you an even number that is equal to the number of digits that are being added together, here 100 / 2 = 50 .
Square the sum. The last step is to square the number, or multiply it by itself. Once you do this, you will have your answer.Here 50×50 =2500. This means the sum of all consecutive odd numbers between 1 and 100 is 2500.