Question

Find the ${12}^{th}$ term of the series $1^2.2+2^2.3+3^2.4+-------\infty$

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Answer 1

$1^2.2+2^2.3+3^2.4+-------\infty$

$n^{th}$ term of the above given series = {$n^{th}termofseries{1}^2,2^2,3^2..........$} $\times$ {$n^{th}$ term of series 2,3,4.......... }

= $n^2.(n+1)$

For ${12}^{th}$ term, substitute n =12

$T_{12}$ = ${12}^2$ $\times$ 13 = 144 $\times$ 13

= 1872