The term independent of x in the expansion of 1-xn1-1-xn isA- C02-2 C12-3 C22- -n-1 Cn2B- C0-c1-cn2C- c02-C12- -cn2D- None of the above

The correct option is C (1+x)^n (1+1/x )^n=(c_0+c_1x+c_2x^2+.....+c_nx^n)×(C_0+C_1/x+C_2/x^2+...+C_n/x^n ) Term independent of x on the RHS =C_0^2+C_1^ ...

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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 $(1 + x)^{n} {(1 + \frac{1}{x})}^{n}$ is

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Solution

The correct option is C
$(1 + x)^{n} {(1 + \frac{1}{x})}^{n} = (c_{0} + c_{1} x + c_{2} x^{2} + . . . . . + c_{n} x^{n}) \times (C_{0} + \frac{C_{1}}{x} + \frac{C_{2}}{x^{2}} + . . . + \frac{C_{n}}{x^{n}}) T e r m i n d e p e n d e n t o f x o n t h e R H S = C_{0}^{2} + C_{1}^{2} + C_{2}^{2} + . . . . + C_{n}^{2}$

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Similar questions

Q. Prove that [1 + (n + 1) x]

(1 + x)^{n - 1}

= C_{0} + 2 C_{1} x + 3 C_{2} x^{2} + . . . + (n + 1) C_{n} x^{n}

and

C_{0}^{2} + 2 C_{1}^{2} + 3 C_{2}^{2} + . . . (n + 1) C_{n}^{2}

= \frac{(n + 2) (2 n - 1)!}{n! (n - 1)!}

Q. If

c_{0}, c_{1}, c_{2}, . . . . . . . c_{n}

denote the coefficients in the expansion of

{(1 + x)}^{n}

, prove that

{c_{0}}^{2} + {c_{1}}^{2} + {c_{2}}^{2} + . . . . {c_{n}}^{2} = \frac{| 2 n - - -}{| n - - | n - -}

Q. A.

^{2 n} C_{n} = C_{0}^{2} + C_{1}^{2} + C_{2}^{2} + C_{3}^{2} + \dots \dots + C_{n}^{2}

^{2 n} C_{n} =

term independent of

x

(1 + x)^{n} {(1 + \frac{1}{x})}^{n}

^{2 n} C_{n} = \frac{1.3.5.7 \dots \dots (2 n - 1)}{n!}

then

{C_{0}}^{2} + \frac{1}{2} {C_{1}}^{2} + \frac{1}{3} {C_{2}}^{2} + . . . . \frac{1}{n + 1} {C_{n}}^{2}

equals

If $(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + . . . . . . . . + C_{n} x^{2}$ , then

$C_{0}^{2} + C_{1}^{2} + C_{2}^{2} + C_{3}^{2} + . . . . . . . . . . + C_{n}^{2}$ =

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The term independent of x in the expansion of (1+x)n(1+1x)n is

The correct option is C (1+x)n(1+1x)n=(c0+c1x+c2x2+.....+cnxn)×(C0+C1x+C2x2+...+Cnxn)Term independent of x on the RHS=C20+C21+C22+....+C2n

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