The coefficient of $x^{m}$ in : ${(1 + x)}^{m} + {(1 + x)}^{m + 1} + . . . . + {(1 + x)}^{n}, m \leq n$ is

{^{n + 1} C}_{m + 1}

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{^{n - 1} C}_{m - 1}

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{^{n} C}_{m}

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{^{n} C}_{m + 1}

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Solution

The correct option is A ${^{n + 1} C}_{m + 1}$
The coefficient of $x^{m}$ will be summation of
$^{m} C_{m} +^{m + 1} C_{m} +^{m + 2} C_{m} . . .^{n} C_{m}$
Upon simplifying we get
$^{n + 1} C_{m + 1}$

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