The sum 1(1!) + 2(2!) + 3(3!) + ........ + n(n!) equals

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Solution

The correct option is C

$S_{π}$ = 1(1!) + 2(2!) + 3(3!) + ...... + n(n!)

= (2 - 1)(1!) + (3 -1)(2!) + (4 - 1)(3!) + .......+ [(n+1) - 1](n!)

= (2.1! - 1!) + (3.2! - 2!) + (4.3! - 3!) + ...... + [(n+1)(n!) - (n!)]

= (2! - 1!) + (3! - 2!) + (4! - 3!) + ..... + [(n+1)! - (n)!]

= (n+1)! - 1!.

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Similar questions

[AMU 1999; DCE 2005]

lim n \to \infty {(\frac{1^{1} \cdot 2^{2} \cdot 3^{3} . . . . . (n - 1)^{n - 1} \cdot n^{n}}{n^{1 + 2 + 3 + . . . . + n}})}^{\frac{1}{n^{2}}}

lim n \to \infty \frac{1^{1} + 2^{2} + 3^{3} + \dots + n^{n}}{1^{n} + 2^{n} + 3^{n} + \dots + n^{n}}

1 + \frac{1 + 2}{2} + \frac{1 + 2 + 3}{3} + . . . .

\frac{n (n + 3)}{4}

\frac{n (n + 2)}{4}

\frac{n (n + 1) (n + 2)}{6}

11 + 22 + 33 + . . . n^{2}

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