What is the difference between the sum of the even integers from 1–100 and the sum of the odd integers from 1–100?

A 0
B 25
C 26
D 50
E 52
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First even integer 2, last one 100
\(\frac{100-2}{2}\)+1=50 even integers
Average of these 50 even integers \(\frac{100+2}{2}\)=51
Sum of even integers=average*number of even int=51*50

First odd integer 1, last one 99
\(\frac{99-1}{2}\)+1=50 odd integers
average of these odd integers \(\frac{99+1}{2}\)=50
Sum of odd integers=average*number of odd int=50*50

difference between the sum of even and odd integers
51*50-50*50=50(51-50)=50

Imo
Ans: D

1 to 100, 50 even & 50 odd

Apart from that 1st even number 2 to 100

1st odd number 1 to last odd number 99

Sn = n/2 (1st term + last term), since the series will be an AP

Sn(even) = 50/2 * 102
= 50 * 51

Sn(odd) = 50/2 * 100
= 50 * 50

Difference = 50 * (51 - 50)
=50

D
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