Question

Find the sum of all the integers from 1 to 100 inclusive that are not
Multiples of 7.

Answer 1

Explanation:

`\text{Denote The sum of all the integers from 1 to 100 inclusive that are NOT multiples of 7 as } S.`

`\text{Denote The sum of all the integers from 1 to 100 inclusive that are multiples of 7 as } P.`

`\text{Denote The sum of all the integers from 1 to 100 inclusive as } Q.`

Then

`\begin{align}S&=Q-P\\&=(100(100+1))/(2)-(7+2\cdot7+\ldots+14\cdot7)\\&=(100(100+1))/(2)-7\cdot(14(14+1))/(2)\\&=4315\end{align}`