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

MCQ

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

A
$3\,(n\,!)\, + \,n - 3$
B
$(n + 1)!\, - \,(n - 1)!$
✓
$(n + 1)\,!\, - 1$
D
$2\,(n\,!) - 2n - 1$

✓

Answer

Correct option: C.

$(n + 1)\,!\, - 1$

c
(c) ${S_n} = 1(1!) + 2(2!) + 3(3!) + ..... + n(n!)$

=$(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!)]$

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

= $(n + 1)! - 1!$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from 8. sequence and series→8. sequence and series — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $3^{2 \sin 2 \alpha-1},14$ and $3^{4-2 \sin 2 \alpha}$ are the first three terms of an $A.P.$ for some $\alpha$, then the sixth term of this $A.P.$ is

Let $x=(\sqrt{50}+7)^{1 / 3}-(\sqrt{50}-7)^{1 / 3}$. Then,

If in the expansion of ${(1 + x)^m}{(1 - x)^n}$, the coefficient of $x$ and ${x^2}$ are $3$ and $-6$ respectively, then m is

Two dice are thrown the events A, B, C are as follows A: Getting an odd number on the first die. B: Getting a total of 7 on the two dice. C: Getting a total of greater than or equal to 8 on the two dice. Then AUB is equal to

If $|x|\, < 1$, then the sum of the series $1 + 2x + 3{x^2} + 4{x^3} + ...........\infty $ will be

The distance between the lines $3x + 4y = 9$ and $6x + 8y = 15$ is

$A, B, C$ are the angles of a triangle, then ${\sin ^2}A + {\sin ^2}B + {\sin ^2}C - 2\cos A\,\cos B\,\cos C = $

The number of ways in which $6$ rings can be worn on the four fingers of one hand is

If one root of the equation ${x^2} + px + q = 0$is the square of the other, then

Selection of menu, food, clothes, subjects, the team are examples of combinations: