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Question

1+1.1!+2.2!+3.3!+...+n.n! is equal to

A
n!
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B
(n1)!
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C
(n+1)!
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D
n
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Solution

The correct option is C (n+1)!
1+1.1!+2.2!+3.3!+...+n.n!
=1+(2.1!1!)+(3.2!2!)+(4.3!3!)+.....((n+1).n!n!)
=1+(2.1!+3.2!+4.3!+....+(n+1).n!)(1!+2!+3!+...+n!)
=1+(2!+3!+4!+.....+(n+1)!)(1!+2!+3!+...+n!)
=1+(n+1)!1=(n+1)!

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