Arithmetic series

Sum of a sequence with constant difference — and the n(n+1)/2 trick.

An arithmetic series adds terms with a constant difference d.

Sum of first n terms

Sₙ = n/2 · (2a + (n−1)d)

Try it

Sum 1 + 2 + 3 + ... + 100

n=100, a=1, d=1. S = 100/2 · (2 + 99) = 50 · 101 = 5050.