(C) We know the binomial expansion: $(1 + x)^n = \sum_{k=0}^{n} \binom{n}{k} x^k = \binom{n}{0} + x\binom{n}{1} + x^2\binom{n}{2} + \dots + x^n\binom{

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(C) We know the binomial expansion: $(1 + x)^n = \sum_{k=0}^{n} \binom{n}{k} x^k = \binom{n}{0} + x\binom{n}{1} + x^2\binom{n}{2} + \dots + x^n\binom{n}{n}$.By substituting $x = 2$ into the expansion,we get:$(1 + 2)^n = \binom{n}{0} + 2\binom{n}{1} + 2^2\binom{n}{2} + \dots + 2^n\binom{n}{n}$.Therefore,the given expression is equal to $3^n$.

Class 11 Mathematics Binomial Theorem Expansion of binomial theorem

Medium

$\binom{n}{0} + 2\binom{n}{1} + 2^2\binom{n}{2} + \dots + 2^n\binom{n}{n}$ is equal to

A
$2^n$
B
$0$
C
$3^n$
D
None of these

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Binomial Theorem

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Expansion of binomial theorem

Find an approximation of $(0.99)^{5}$ using the first three terms of its binomial expansion.

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The number of non-zero terms in the expansion of $(1 + 3\sqrt{2}x)^9 + (1 - 3\sqrt{2}x)^9$ is

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If the sum of odd terms is $A$ and the sum of even terms is $B$ in the expansion of $(x + a)^n$,then:

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The coefficient of $x^4$ in the expansion of $(1+x-x^2-x^3)^{11}$ is

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The coefficient of $x^8$ in the expansion of $(x-1)(x-2)(x-3)\ldots(x-10)$ is:

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$\binom{n}{0} + 2\binom{n}{1} + 2^2\binom{n}{2} + \dots + 2^n\binom{n}{n}$ is equal to

Similar Questions

Find an approximation of $(0.99)^{5}$ using the first three terms of its binomial expansion.

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