Number of dissimilar terms in the expansion of $(x_{1} + x_{2} + . . . . . + x_{n})^{3}$ is

\frac{n^{2} (n + 1)^{2}}{4}

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

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^{n + 1} C_{2} +^{n} C_{2}

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\frac{n^{3} + 3 n^{2}}{4}

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Solution

The correct options are
B $\frac{n (n + 1) (n + 2)}{6}$
C $^{n + 1} C_{2} +^{n} C_{2}$
The number of dissimilar terms in the expression
$=^{3 + n - 1} C_{3}$
$=^{n + 2} C_{3}$
$= \frac{(n + 2) . (n + 1) . n}{3!}$
$= \frac{n (n + 1) (n + 2)}{6}$ .

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{(x_{1} + x_{2} + . . . . . . + x_{n})}^{3}

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