Ish1996 wrote:
Bunuel wrote:
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
I dont understand why this doesnt work:
sum of first n even numbers = n(n+1)
sum of first odd numbers = n^2
100(101) - 100^2 = 100
Can someone explain why this formula wont work?
The reason why this method is not working is because the value of n that you have assumed is incorrect.
The even integers form the following series: 2,4,6,8...100
Hence it is an AP with common difference 2
We know in an AP, L=a + (n-1)d..; L is the last term. In this case: 100
100=2+(n-1)2
n=50
Similarly for odd terms n = 50
Using ur method again, we get
n(n+1)-n^2
=>50 x 51 - 50^2
=>50(51-50)
=>50 x 1
=> 50
Hence option D