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SEQUENCES AND SERIES — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSEQUENCES AND SERIES1 Mark
Question
Find the sum to n terms of the series whose n th term is n (n+3).
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Answer

Given that $a_n = n (n + 3) = n^2 + 3n$
Therefore,the sum to n terms is given by
$\mathrm{S}_{n}=\sum_{k=1}^{n} a_{k}=\sum_{k=1}^{n} k^{2}+3 \sum_{k=1}^{n} k$
= $\frac{n(n+1)(2 n+1)}{6}+\frac{3 n(n+1)}{2}$ = $\frac{n(n+1)(n+5)}{3}$

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