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1.1!+2.2!+3.3!+.......n.n!` is equal toA. `(n+1)!`B. `(n+1)!+1`C. `(n+1)!-1`D. none of these

Answer» Correct Answer - C
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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