The middle term in the expansion of x-1-x2 n isA- 2 nOB- 2 -n Cn-2C- 2 n Cn-1D- 2 -2 n Cn-1

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Middle Terms

The middle te...

Question

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

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Solution

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

Find the sum of the series $^{n} C_{0}^{n} C_{2} +^{n} C_{1}^{n} C_{3} +^{n} C_{2}^{n} C_{4} . . . . .^{n} C_{n - 2}^{n} C_{n}$

^{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} =

x

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

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

(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 {(C_{r} + C_{s})}_{r}^{2}

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

\sum \sum 0 \leq r < s \leq n C_{r} C_{s}

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