Track / Stage 4 / 251 of 340 #511 of 2000

Problem 511

AMC 12 late, AIME early

Algebra Difficulty 4.9 Find the answer

7. The function $f$ defined on the set of positive integers $\mathbf{N}^{-}$ satisfies: $f(1)=1$ , and for any natural numbers $m, n$ , $f(m)+$ $f(n)=f(m+n)-m n$ , then $f(m)=$ $\qquad$ .

Your answer

Official solution

7. $\frac{m(m+1)}{2}$ Let $n=1, f(m+1)-f(m)=m+1$ , then use partial fraction decomposition.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.