If 1-xn-C0-c1 x-Cn xn- then C1-C0-2 C2-C1-3 C 3-C2- - - nC n-Cn-1 isA- 2n-n-B- n -n-1-2nn-1-2D- n-1n-n -

The correct option is C C_1/C_0+2C_1/C_1+3C_3/C_2+.....nC_n/C_n 1 =n/1/1+2.1(1 1)/1 2/n/1+3.n(n 1)( 2)/1.2.3/1(n 1)/1.2+....+n.1/n/1 =n+(n 1)+(n 2)+....+1 = ...

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Byju's Answer

Standard XII

Mathematics

Greatest Binomial Coefficients

If 1+xn=C0+c1...

Question

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

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Solution

The correct option is D
$\frac{C_{1}}{C_{0}} + \frac{2 C_{1}}{C_{1}} + \frac{3 C_{3}}{C_{2}} + . . . . . \frac{n C_{n}}{C_{n - 1}} = \frac{\frac{n}{1}}{1} + \frac{2. \frac{1 (1 - 1)}{1 - 2}}{\frac{n}{1}} + \frac{3. \frac{n (n - 1) (- 2)}{1.2.3}}{\frac{1 (n - 1)}{1.2}} + . . . . + \frac{n .1}{\frac{n}{1}} = n + (n - 1) + (n - 2) + . . . . + 1 = 1 + 2 + 3 + . . . . + n = \frac{n (n + 1)}{2}$

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Similar questions

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

$\frac{C_{1}}{C_{0}}$ + $\frac{2 C_{2}}{C_{1}}$ + $\frac{3 C_{3}}{C_{2}}$ + ........+ $\frac{n C_{n}}{C_{n - 1}}$ =

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

i 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

Q. If

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

denote the coefficients in the expansion of

{(1 + x)}^{n}

, prove that

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

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If (1+x)n=C0+c1x+...+Cnxn+,then C1C0+2C2C1+3C3C2+.....+nCnCn−1 is

The correct option is D C1C0+2C1C1+3C3C2+.....nCnCn−1=n11+2.1(1−1)1−2n1+3.n(n−1)(−2)1.2.31(n−1)1.2+....+n.1n1=n+(n−1)+(n−2)+....+1=1+2+3+....+n=n(n+1)2

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