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whats the sum of series: 1^5*2^7/1! + 2^5*3^7/2! + 3^5*4^7/3! + 4^5*5^7/4! +......................infinite....

whats the sum of series:


1^5*2^7/1! + 2^5*3^7/2! + 3^5*4^7/3! + 4^5*5^7/4! +......................infinite....

Grade:11

1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
6 years ago
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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