The coefficient of xn in the polynomial x-2 n C0x-2 n C2 -x-2 n C2 n is A- 22 n -1B- 2 n -1C- 2 nD- 22 n -1

The correct option is D 2^2n 1 nbsp;Required coefficient of x^n = ^2nC_0 + ^2nC_2 + ^2nC_4 + ⋯ + ^2nC_2n = 2^2n2 = 2^2n 1 ...

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Sum of Coefficients of All Terms

The coefficie...

Question

The coefficient of $x^{n}$ in the polynomial $(x +^{2 n} C_{0}) (x +^{2 n} C_{2}) \dots (x +^{2 n} C_{2 n})$ is

2^{2 n - 1}

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2^{2 (n - 1)}

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2^{n}

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2^{n - 1}

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Solution

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Similar questions

In the expansion of $(1 + x)^{n}$ the sum of coefficients

of odd powers of x is

x^{n}

(x + {^{2 n + 1} C}_{0}) (x + {^{2 n + 1} C}_{1}) (x + {^{2 n + 1} C}_{2}) + . . . . (x + {^{2 n + 1} C}_{n})

x^{n - 1}

(x +^{2 n + 1} C_{0}) (x +^{2 n + 1} C_{1}) (x +^{2 n + 1} C_{2}) \dots (x +^{2 n + 1} C_{n})

\sum_{r = 1}^{n} r .^{2 n} C_{r}

(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + \dots + C_{n} x^{n},

\sum \sum 0 \leq r < s \leq n (r + s) C_{r} C_{s}

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