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If S(n)=(1^(2)-1+1)(1!)+(2^(2)-2+1)(2!)+...

If `S_(n)=(1^(2)-1+1)(1!)+(2^(2)-2+1)(2!)+...+(n^(2)-n+1)(n!)`, then `S_(50)=`

A

`52!`

B

`1+49xx5!`

C

`52!-1`

D

`50xx51!-1`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `T_(n)=(n^(2)-n+1)n!`
`=(n^(2)-1)n!-(n-2)n!`
`T_(n)=(n-1)(n+1)!-(n-2)n!`
`:. S_(n)=1+(n-1)(n+1)!`
`:.S_(30)=1+49xx51!`
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