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find the sum of the given series. description given in the image

find the sum of the given series.
description given in the image

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Grade:12th pass

2 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
7 years ago
PFA
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mycroft holmes
272 Points
7 years ago
(r2+1) . r! = (r2+2r+1).r! -2r.r! = (r+1)2r! – 2r.r! = (r+1) (r+1)r! – 2r.r!
 
= (r+1).(r+1)! – r.r! – r.r!
 
=[(r+1).(r+1)! – r.r!] – [(r+1)! – r!]
 
Thus, the summation is seen to be sum of two telescoping series.
 
The required sum is easily obtained as (n+1). (n+1)! – (n+1)! = n.(n+1)!

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