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