# Find the nth Partial Sum Sn of the series sum 1(2kappa −1)(2kappa +1) kindly solve fast.

Find the nth Partial Sum Sn of the series
$\sum 1\left(2\kappa -1\right)\left(2\kappa +1\right)$
kindly solve fast.
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Obiajulu
$\sum _{k=1}^{k=n}1\left[\left(2k-1\right)\left(2k+1\right)\right]$
$\sum _{k=1}^{k=n}1\left[4\left({k}^{2}\right)-1\right]$
$\sum _{k=1}^{k=n}\left[4\left({k}^{2}\right)\right]-\sum \left[1\right]$
$4\sum _{k=1}^{k=n}\left[{k}^{2}\right]-\sum \left[1\right]$
$4\left({1}^{2}\right)+{2}^{2}+{3}^{2}+\dots +{n}^{2}\right)-\left(1+2+3+\dots +n\right)$
Sum of square of natural number =$\frac{n\left(n+1\right)\left(2n+1\right)}{6}$
Sum of natural number =$\frac{n\left(n+1\right)}{2}$
$\frac{4n\left(n+1\right)\left(2n+1\right)}{6}-\frac{n\left(n+1\right)}{2}$
$\frac{n\left(n+1\right)}{2}×\left[\frac{4\left(2n+1\right)}{3}-1\right]$
$\frac{n\left(n+1\right)}{2}\left[\frac{8n+4-3}{3}\right]$
$\frac{n\left(n+1\right)}{2}\left[\frac{8n+1}{3}\right]$
$\frac{n\left(n+1\right)\left(8n+1\right)}{6}$
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