What is the difference between the sum of all positive odd integers less than 102 and the sum of all positive even integers less than 102

Asked by Navpankaj Jain | 12th Dec, 2013, 07:33: PM

Expert Answer:

We have,101<102
 
Therefore, the first 101 integers consist of 50 even numbers and 51 odd numbers.
 
Sum of odd numbers = 1 + 3 + 5 + 7 + ... + 95 + 97 + 99 + 101
 
Sum of even numbers =      2 + 4 + 6 + ... + 94 + 96 + 98 + 100 
 
Difference                    1 + 1 + 1 + 1 + ... + 1    + 1  +  1  +  1
 
There are 51 odd numbers.
 
Therefore, the difference is 51.

Answered by Vimala Ramamurthy | 12th Dec, 2013, 09:37: PM

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