The coefficient of xm in 1-x m - 1-m m-1 - 1-x n -m- n is

The correct option is C ^ n+1 C _ m+1 ^ #160; The coefficients of x _ m in ( 1+x ) #160;^ m =( 1+x ) #160;^ m+1 +( 1+x ) #160;^ m+2 + ...

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Implicit Differentiation

The coefficie...

Question

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

^{n} C_{m}

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^{n} C_{m + 1}

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

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None of these

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

x^{m}

{(1 + x)}^{m} + {(1 + x)}^{m + 1} + . . . . + {(1 + x)}^{n}, m \leq n

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

y = \frac{1}{1 + x^{n - m} + x^{p - m}} + \frac{1}{1 + x^{m - n} + x^{p - n}} + \frac{1}{1 + x^{m - p} + x^{n - p}}, t h e n \frac{d y}{d x}

x^{m}

(1 + x)^{m} + 2 (1 + x)^{n - 1} + 3 (1 + x)^{n - 2} + (n - m + 1) (1 + x)^{m}

0 \geq m \geq n i s^{n + 2} C_{m + 2}

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