Sum of the series `sum_(r=1)^n (r^2+1)r!,` isA. `(n+1)!`B. `(n+2)!-1`C. `n(n+1)!`D. none of these

Sum of the series `sum_(r=1)^n (r^2+1)r!,` isA. `(n+1)!`B. `(n+2)!-1`C

1.	Sum of the series `sum_(r=1)^n (r^2+1)r!,` isA. `(n+1)!`B. `(n+2)!-1`C. `n(n+1)!`D. none of these
Answer» We have, `sum_(r=1)^(n)(r^(2)+1)r!` `sum_(r=1)^(n){(r+2)(r+1)-3(r+1)+2}r!` `sum_(r=1)^(n){(r+2)!-(r+1)!}-2sum_(r=1)^(n){(r+1)!-r!}` `=(n+2)!-2!-2{(n +1)!-1}=n(n+1)!`

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Sum of the series `sum_(r=1)^n (r^2+1)r!,` isA. `(n+1)!`B. `(n+2)!-1`C. `n(n+1)!`D. none of these

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