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General Term of Binomial Expansion

If C 0, C 1, ...

Question

If $C_{0}, C_{1}, C_{2}, . . . . . C_{n}$ denote the coefficient in the expansion of $(1 + x)^{n}$ , then the value of $C_{1} + 2 C_{2} + 3 C_{3} . . . . + n C_{n}$ is

A

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B

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C

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D

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Solution

The correct option is A
$I n (1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + . . . . . . + C_{n} x^{n} D i f f e r e n t i a t e b o t h s i d e s w . r . t . x n (1 + x)^{n - 1} = C_{1} + 2 C_{2} x + . . . . + n C_{n} x^{n - 1}, p u t x = 1 n {.2}^{n - 1} = C_{1} + 2 C_{2} x + . . . . + n C_{n}$

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Similar questions

C_{0}, C_{1}, C_{2}, . . . . . . . C_{n}

denote the coefficients in the expansion of

{(1 + x)}^{n}

C_{1} + 2 C_{2} + 3 C_{3} + . . . . n C_{n} = n . {(2)}^{n - 1}

c_{0}, c_{1}, c_{2}, . . . . . c_{n}

denote the coefficients in the expansion of

(1 x)^{n}

c_{1} + 2 c_{2} + 3 c_{3} + . . . . . . + n c_{n} = n {.2}^{n - 1}

I f (1 + x)^{n} = C_{0} + c_{1} x + . . . + C_{n} x^{n} +, t h e n \frac{C_{1}}{C_{0}} + \frac{2 C_{2}}{C_{1}} + \frac{3 C_{3}}{C_{2}} + . . . . . + \frac{n C_{n}}{C_{n - 1}} i s

C_{0}, C_{1}, C_{2} . . . ., C_{n}

denote the binomial coefficients in the expansion of

{(1 + x)}^{n}

\frac{C 1}{C 0} + 2 \frac{C 2}{C 1} + + 3 \frac{C 3}{C 2} + . . . . . + n \frac{C n}{C n - 1}

C_{0}, C_{1}, C_{2}, \dots, C_{n}

denote the coefficients in the expansion of

{(1 + x)}^{n}

, then the value of

C_{1} + 2 C_{2} + 3 C_{3} + \dots + n C_{n}

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