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JEE Main 2026 · 5 Apr · Shift 1, Mathematics question 5

∑n=110(528n(n+1)(n+2))\displaystyle\sum_{n=1}^{10}\left(\frac{528}{n(n+1)(n+2)}\right) is equal to:

Choose one option
Answer and worked solution

Official answer: B

Telescoping.
1n(n+1)(n+2)=12[1n(n+1)−1(n+1)(n+2)].\frac1{n(n+1)(n+2)}=\frac12\left[\frac1{n(n+1)}-\frac1{(n+1)(n+2)}\right].
∑n=110=12[12−1132]=65264.\sum_{n=1}^{10}=\frac12\left[\frac12-\frac1{132}\right]=\frac{65}{264}.

Times 528: 130130.

(B)

Topics:Special series sums
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