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MATH / Consider the sequence defined by a_(k)=(1)/(k²+k) for k≥1. Given that a_(m)+a_(m+1)+⋯+a_(n−1)=(1)/(29), for positive integers m and n with m<n, find m+n.

Problem

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problem

Consider the sequence defined by ak=1k2+ka_k=\frac 1{k^2+k} for k≥1k\ge 1. Given that am+am+1+⋯+an−1=129a_m+a_{m+1}+\cdots+a_{n-1}=\frac{1}{29}, for positive integers mm and nn with m<nm<n, find m+nm+n.
Plain-text mathematical notation (without MathML)
Consider the sequence defined by a_(k)=(1)/(k²+k) for k≥1. Given that a_(m)+a_(m+1)+⋯+a_(n−1)=(1)/(29), for positive integers m and n with m<n, find m+n.
Original LaTeX notation
Consider the sequence defined by $a_k=\frac 1{k^2+k}$ for $k\ge 1$. Given that $a_m+a_{m+1}+\cdots+a_{n-1}=\frac{1}{29}$, for positive integers $m$ and $n$ with $m<n$, find $m+n$.

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
e7ac750b-53ef-5135-a430-98295b8dbd7e
task_key
intermediate~5falgebra--test--e7ac750b-53ef-5135-a430-98295b8dbd7e
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import