The term independent of x in the expansion of x-1-x-2 m is-A- 2 m CmB- 2 m Cm-1- 2 m Cm-1-1D- 2 m Cm-1

The correct option is A (x+1 x+2)^m=(x^2+1+2x)^m/x^m =(x+1)^2m/x^m The term independent of x in (x+1)^2m/x^m will be the term which has x^m in (x+1)^2m, which ...

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Byju's Answer

Standard XI

Mathematics

Term Independent of X

The term inde...

Question

The term independent of x in the expansion of $(x + \frac{1}{x} + 2)^{m}$ is:

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Solution

The correct option is A

$(x + \frac{1}{x} + 2)^{m} = \frac{(x^{2} + 1 + 2 x)^{m}}{x^{m}}$
= $\frac{(x + 1)^{2 m}}{x^{m}}$
The term independent of x in $\frac{(x + 1)^{2 m}}{x^{m}}$ will be the term which has $x^{m}$ in $(x + 1)^{2 m}$ , which is $^{2 m} C_{m}$ .

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The term independent of x in the expansion of (x+1x+2)m is:

The correct option is A (x+1x+2)m=(x2+1+2x)mxm =(x+1)2mxm The term independent of x in (x+1)2mxm will be the term which has xm in (x+1)2m, which is 2mCm.

The term independent of x in the expansion of $(x + \frac{1}{x} + 2)^{m}$ is:

The correct option is A

$(x + \frac{1}{x} + 2)^{m} = \frac{(x^{2} + 1 + 2 x)^{m}}{x^{m}}$
= $\frac{(x + 1)^{2 m}}{x^{m}}$
The term independent of x in $\frac{(x + 1)^{2 m}}{x^{m}}$ will be the term which has $x^{m}$ in $(x + 1)^{2 m}$ , which is $^{2 m} C_{m}$ .