The number of terms in the expansion of (a + | vedclass

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(C) The number of terms in the expansion of $(x_1 + x_2 + \dots + x_k)^n$ is given by the formula $\binom{n + k - 1}{k - 1}$.Here,$k = 3$ (terms $a, b

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) The number of terms in the expansion of $(x_1 + x_2 + \dots + x_k)^n$ is given by the formula $\binom{n + k - 1}{k - 1}$.Here,$k = 3$ (terms $a, b, c$) and the power is $n$.Therefore,the number of terms is $\binom{n + 3 - 1}{3 - 1} = \binom{n + 2}{2}$.Expanding the combination formula: $\binom{n + 2}{2} = \frac{(n + 2)(n + 2 - 1)}{2 	imes 1} = \frac{(n + 2)(n + 1)}{2}$.Thus,the correct option is $C$.

The number of terms in the expansion of $(a + b + c)^n$ will be

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