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The value of 1*1!+2*2!+3*3!+…+N*N! is...

The value of `1*1!+2*2!+3*3!+…+N*N! ` is

A

`(n+1)!`

B

`(n+1)!+1`

C

`(n+1)!-1`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
b
We have , `1*1! +2*2 ! + 3*3 ! +…+n*n!`
` sum_(r=1)^(n) r*(r!) = sum_(r=1)^(n) [(r+1)r!-r!] = sum_(r=1)^(n) [(r+1)!-r!]`
` = (2!-1!) + (3!-2!) +...= [(n+1)!-n!]`
` = (n+1)! - 1! = (n+1)! -1`
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  1. The value of 1*1!+2*2!+3*3!+…+N*N! is

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