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Question

The value of 1.1!+2.2!+3.3!+..........+n.n!, is

A
(n+1)!
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B
(n+1)!+1
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C
(n+1)!1
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D
None of these
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Solution

The correct option is C (n+1)!1
S=1.1!+2.2!.......................n.n!
=(21)1!+(31)2!....................(n+11)n!
=2.1!1.1!+3.2!2!................(n+1)n!n!
=2!1!+3!2!.........................(n+1)n!n!
=(n+1)!1

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