The value of C12-C34-C56- is equals-

The correct option is A 2^n+1n 1 ...

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Applications of Dot Product

The value of ...

Question

The value of $\frac{C_{1}}{2} + \frac{C_{3}}{4} + \frac{C_{5}}{6} + . . . .$ is equals?

\frac{2^{n} + 1}{n - 1}

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\frac{2^{n}}{n + 1}

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\frac{2^{n} + 1}{n + 1}

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\frac{2^{n} - 1}{n + 1}

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\frac{C_{1}}{2} + \frac{C_{3}}{4} + \frac{C_{5}}{6} + . . . = \frac{2^{n} - 1}{n + 1}

\frac{C_{1}}{2} + \frac{C_{3}}{4} + \frac{C_{5}}{6} + . . . . = \frac{2^{n} - 1}{n + 1}

1 - 2 n + \frac{2 n (2 n - 1)}{2!} - \frac{2 n (2 n - 1) (2 n - 1)}{3!} + . . . + (- 1)^{n - 1} \frac{2 n (n - 1) . . . (n + 2)}{(n - 1)}

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

C_{0} + \frac{C_{1}}{2} + \frac{C_{2}}{3} + \frac{C_{3}}{4} + . . . . + \frac{C_{n}}{n + 1} = \frac{2^{n + 1} - 1}{(n + 1)}

a = \infty \sum n = 1 \frac{2 n}{(2 n - 1)!}, b = \infty \sum n = 1 \frac{2 n}{(2 n + 1)!}

a b

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