1 + 1 3 x + 1.4 3.6 x^2 + 1.4.7 3.6.9 x^3 + .... is equal to - Vidyadip

MCQ

$1 + \frac{1}{3}x + \frac{{1.4}}{{3.6}}{x^2} + \frac{{1.4.7}}{{3.6.9}}{x^3} + .... $ is equal to

A
$x$
B
${(1 + x)^{1/3}}$
C
${(1 - x)^{1/3}}$
✓
${(1 - x)^{ - 1/3}}$

✓

Answer

Correct option: D.

${(1 - x)^{ - 1/3}}$

d
(d) Let ${(1 + y)^n} = 1 + \frac{1}{3}x + \frac{{1.4}}{{3.6}}{x^2} + \frac{{1.4.7}}{{3.6.9}}{x^3} + ....$

$ = 1 + ny + \frac{{n(n - 1)}}{{2!}}{y^2} + .....$

Comparing the terms, we get

$ny = \frac{1}{3}x,\frac{{n(n - 1)}}{{2!}}{y^2} = \frac{{1.4}}{{3.6}}{x^2}$

Solving, $n = - \frac{1}{3},y = - x$.

Hence given series $ = {(1 - x)^{ - 1/3}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from binomial theoram→binomial theoram — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The coefficient of y in the expansion of $\Big(\text{y}^2+\big(\frac{\text{c}}{\text{y}}\big)\Big)^5$ is:

If the ${9^{th}}$ term of an $A.P.$ is $35$ and ${19^{th}}$ is $75$, then its ${20^{th}}$ terms will be

If A and B are two disjoint sets, then $\text{n(A}\cup\text{B)}$ is equal to:

$\text{n(A) + n(B)}$
$\text{n(A) + n(B)} - \text{n(A}\cap\text{B)}$
$\text{n(A) + n(B) + n(A}\cap\text{B)}$
$\text{n(A) n(B)}.$

If $p$ times the ${p^{th}}$ term of an $A.P.$ is equal to $q$ times the ${q^{th}}$ term of an $A.P.$, then ${(p + q)^{th}}$ term is

Complete 2, 3, 5, 7, ________.

Define a sequence $\left\langle a_n\right\rangle$ by $a_1=5, a_n=a_1 a_2 \ldots a_{n-1}+4$ for $n > 1$. Then, $\lim _{n \rightarrow \infty} \frac{\sqrt{ a _n}}{ a _{n-1}}$

Integers $1,2,3, \ldots \ldots, n,(n \geq 3)$ are written on a black board and an integer $k (1 < k < n )$ is erased. The average of the remaining numbers is $16$ . Then $n + k$ is

If − 3x + 17 < -13, then:

If the equations $\text{x}^2+2\text{x}+3\lambda=0$ and $2\text{x}^2+3\text{x}+5\lambda=0$ have a non-zero common roots, then $\lambda=$

Six boys and six girls sit in a row randomly. The probability that the six girls sit together