The term independent of x in 1-x m 1- 1 - x n is

The correct option is C ^ m+n C _ n (1+x)^m(1+1x)^n =(1+x)^nx^n.(1+x)^m =(1+x)^m+nx^n Writing the general expression for any term in the a ...

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Term Independent of x

The term inde...

Question

The term independent of $x$ in ${(1 + x)}^{m} {(1 + \frac{1}{x})}^{n}$ is

^{m + n} C_{m}

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^{m + n} C_{n}

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^{m + n} C_{m - n}

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None of these

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x^{m}

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

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

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

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}}

\frac{d y}{d x}

e^{m^{n^{p}}}

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