Question

sum of all the multiples of 7 between 1 and 200.

Answer 1

Since ⌊200/7⌋ ≈ ⌊28.5714⌋ = 28, there are only 28 terms in the sum:

S = 7 + 14 + 21 + … + 189 + 196

Each term is a multiple of 7, so

S = 7 (1 + 2 + 3 + … + 27 + 28)

Recall that

$\displaystyle \sum_{n=1}^Nn = 1 + 2 + 3 + \cdots + N = \dfrac{N(N+1)}2$

Then

S = 7/2 • 28 • 29 = 2842