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Question

Sum of the series nr=1(r2+1)r! is

A
(n+1)!
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B
(n+2)!1
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C
n(n+1)!
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D
n(n+2)!
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Solution

The correct option is C n(n+1)!
We check it by putting the different values of n
Let n=2
2r=1(r2+1).r!=2.1!+5.2!=12

Now check it with the options given
A) (n+1)! = 3! =6

B) (n+2)!1 = 4!1 =23

C) n.(n+1)! = 2.3! =12

D) n.(n+2)! = 2.4! =48

Hence C) is the correct answer

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