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Differential Calculus> exponential series...

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whats the sum of series:

1^52^7/1! + 2^53^7/2! + 3^54^7/3! + 4^55^7/4! +......................infinite....

Vivek Raj , 14 Years ago

Grade 11

1 Answers

Sumit Majumdar

Dear student,
The general term of the series can be given by:
$T_{n}=\frac{n^{5}\left ( n+1 \right )^{7}}{n!}$

So, the required sum can be found as:
$S_{n}=\sum_{1}^{\infty}T_{n}=\sum_{1}^{\infty}\frac{n^{5}\left ( n+1 \right )^{7}}{n!}$
Using the standard formulae, the required sum can be found.
Regards
Sumit

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