If 1-xn-C0-C1x-C2x2- -Cnxn then C0-1-C2-3-C4-5- - -

The correct option is D 2^n/n+1 The above expression is nothing but nbsp; 12∫_x=0 ^x=1 [(1+x)^n+(1 x)^n].dx =12[(1+x)^n+1 (1 x)^n+1n+1]_x=0 ^x= ...

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Higher Order Derivatives

If 1+xn=C0+...

Question

If $(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + . . . + C_{n} x^{n}$ then $\frac{C_{0}}{1} + \frac{C_{2}}{3} + \frac{C_{4}}{5} + . . . . =$

2^{n}

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

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

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\frac{2^{n}}{n}

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Solution

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Similar questions

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

C_{0} - C_{2} + C_{4} - C_{6} + . . . . . . .

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

C_{0} C_{r} + C_{1} C_{r + 1} + . . . . . . + C_{n - r} C_{n} = \frac{(2 n)!}{(n + r)! (n - r)!}

(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + C_{3} x^{3} + \dots + C_{n} x^{n},

C_{0} C_{2} + C_{1} C_{3} + C_{2} C_{4} + \dots + C_{n - 2} C_{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 (r + s) C_{r} C_{s}

I f (1 + x)^{n} = C_{0} + c_{1} x + . . . + C_{n} x^{n} +, t h e n \frac{C_{1}}{C_{0}} + \frac{2 C_{2}}{C_{1}} + \frac{3 C_{3}}{C_{2}} + . . . . . + \frac{n C_{n}}{C_{n - 1}} i s

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