A student wanted to find the sum of all the even numbers from 1 to 100. He said:

The sum of all the even numbers from 1 to 100 is twice the sum of all the odd numbers from 1 to 100.
The sum of all the odd numbers from 1 to 100 is 100^2.

Explain why each of these statements is incorrect.

Question

A student wanted to find the sum of all the even numbers from 1 to 100. He said:

    The sum of all the even numbers from 1 to 100 is twice the sum of all the odd numbers from 1 to 100.
    The sum of all the odd numbers from 1 to 100 is 100^2.

Explain why each of these statements is incorrect.

thomasfire55 · Answer

@mayankdevnani

mayankdevnani · Answer

1) The sum of all even numbers from 1 to 100 is equal to twice the sum of all integers from 1 to 50.

mayankdevnani · Answer

2) The sum of all odd numbers from 1 to 100 is 
1 + 3 + ...... + 99 
Use Arithmetic progression to find out sum !

mayankdevnani · Answer

The sum of all the odd numbers from 1 to 100 is 2500.