The sum of first 9 terms of the series …… is

Engineering

Mathematics

Geometric Progression and Its Properties

Special Types of Sequence

Summation of Series

Question

The sum of first 9 terms of the series $\frac{1^{3}}{1} + \frac{1^{3} + 2^{3}}{1 + 3} + \frac{1^{3} + 2^{3} + 3^{3}}{1 + 3 + 5} +$ …… is

192

142

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$T_{n} = \frac{{(n + 1)}^{2}}{4}$

$S_{n} = \frac{1}{4} (\frac{n (n + 1) (2 n + 1)}{6} + 2 \frac{n (n + 1)}{2} + n)$

$∴$ S₉ = 96.