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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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