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Question

The sum of the series (12+1).1!+(22+1).2!+(32+1).3!+......+(n2+1).n! is

A
(n+1).(n+2)!
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B
n.(n+1)!
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C
(n+1).(n+1)!
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D
none of these
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Solution

The correct option is A (n+1).(n+2)!
We have
Sn=(12+1).1!+(22+1).2!+(32+1).3!+.....+(n2+1).n!

=12.1!+!+22.2!+2!+32.3!+3!+.......+n2n!+n!

=(n+1)(n+2)!
Hence, the option (A) is correct answer.

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