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Q)

Find the sum of the series upto 20 term 1+(1+2)+(1+2+3)+--------

$\begin{array}{1 1} 1540 \\ 1560 \\ 1770 \\ 1880 \end{array}$

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A)
Answer : (a) 1540
Explanation : $t_{n}=\frac{n(n+1)}{2}$
$S_{n}=\sum\;\frac{n(n+1)}{2}=\frac{1}{2}\;[\sum\;n^2+\sum\;n]$
$=\frac{1}{2}\;[\frac{n(n+1)(2n+1)}{6}+\frac{n(n+1)}{2}]$
$n=20$
$S_{20}=\frac{1}{2}\;[\frac{20*21*41}{6}+\frac{20*21}{2}]$
$=1540.$
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