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

^{n + 1}C_{m + 1}

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^{n - 1}C_{m - 1}

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ⁿC_m

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ⁿC_{m + 1}

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Solution

The correct option is A
^{n + 1}C_{m + 1}

$^{m} C_{m}$ + $^{m + 1} C_{m}$ + $^{m + 2} C_{m}$ + ..........+ $^{n} C_{m}$ = $^{m + 1} C_{m + 1}$ + $^{m + 1} C_{m}$ + $^{m + 2} C_{m}$ + ....+ $^{n} C_{m}$ = $^{n + 1} C_{m + 1}$

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