IIT JEE , AIEEE Forum - Mathematics , Algebra - Arithmatico-Geometric Series

agnit_thebest

Pls. help me in finding the sum of the series:

3/1! + 5/2! + 9/3! + 15/4! + 23/5! + .....................upto infinity

Pls. show the details

nadeemoidu

The general term is (k²-k+3)/ k!

= k(k-1)/ k! + 3/k!

= 1/(k-2)! + 3/k!

now use the expansion of 'e' .

I don't think this is an AGP.

hsbhatt

I hope this is not considered as quibbling on minor matters, but 1/(k-2)! isnt defined for k=1. So for the first sum k runs from 2 onwards. It doesn't change the sum, but just to be more accurate in our presentation.

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