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Problem 523

AMC 12 late, AIME early

Algebra Difficulty 4.9 Find the answer

6. Let positive integers $m, n$ satisfy $m<n$ , and
$\frac{1}{m^{2}+m}+\frac{1}{(m+1)^{2}+(m+1)}+\cdots+\frac{1}{n^{2}+n}=\frac{1}{23} \text {. }$

Then the value of $m+n$ is $\qquad$ .

Your answer

Official solution

$6.527$

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