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  4. The sum of the series 1 + 2 × 3 + 3 × 5+4 × 7 +.... upto 11th term is :-

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Q. The sum of the series$ 1 + 2 \times 3 + 3 \times 5+4 \times 7 +.... $ upto $11^{th}$ term is :-

JEE MainJEE Main 2019Sequences and Series

Solution:

$T_{r} = r\left(2r -1\right) $
$ S = \sum2r^{2} -\sum r $
$ S = \frac{2.n\left(n+1\right)\left(2n+1\right)}{6} - \frac{n\left(n+1\right)}{2}$
$ S_{11} = \frac{2}{6} .\left(11\right)\left(12\right)\left(23\right) - \frac{11\left(12\right)}{2} =\left(44\right)\left(23\right)-66 = 946 $