Skip to content

Adding the whole numbers from 1 to 100

Question

What is 1+2+3+⋯+1001+2+3+\cdots+100? Give also a formula for 1+2+⋯+n1+2+\cdots+n.

Short answer

50505050; in general n(n+1)2\tfrac{n(n+1)}{2}. Write the sum forwards and backwards and add: each of the nn columns totals n+1n+1, so twice the sum is n(n+1)n(n+1). For n=100n=100 that gives 100⋅101/2=5050100\cdot101/2=5050.

Adapted from Crack, Heard on the Street, Q1.3, p.9; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question