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

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.