Home
Class 12
MATHS
If (1)/((1 - 2x)(1 + 3x)) is to tbe expa...

If `(1)/((1 - 2x)(1 + 3x))` is to tbe expanded as a power series of x, then

A

`|x| lt 1//2`

B

`|x| lt 1//6`

C

`-1//3 lt x lt 1//2`

D

`|x| lt 1//3`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of expanding the expression \(\frac{1}{(1 - 2x)(1 + 3x)}\) as a power series of \(x\), we will follow these steps: ### Step 1: Rewrite the Expression We start by rewriting the expression in a form that is easier to expand. We can express it as: \[ \frac{1}{(1 - 2x)(1 + 3x)} = \frac{1}{1 - 2x} \cdot \frac{1}{1 + 3x} \]
Promotional Banner

Similar Questions

Explore conceptually related problems

If (x-4)/(x^(2)-5x+6) can be expanded in the ascending powers of x , then the coefficient of x^(3) is

If (e^(5x)+e^(x))/(e^(3x)) is expand in a series of ascending powers of x and n is and odd natural number then the coefficent of x^(n) is

If the coefficient x^(2) and x^(3) in the expansion of (1 + 8x + bx^(2))(1 - 3x)^(9) in the power of x are equal , then b is :

If the expansion in power of x of the function (1)/(( 1 - ax)(1 - bx)) is a_(0) + a_(1) x + a_(2) x^(2) + a_(3) x^(3) + …, then a_(n) is

Find the value of x , for which 1/(sqrt(5+4x)) can be expanded as infinite series.

Expand (1+ 2 x + 3x^(2) )^(n) in a series of ascending powers of x up to and including the term in x^2 .

The number of terms in the expansion of (1+2x+x^2)^(20) when expanded in decreasing powers of x is

Let n is a rational number and x is a real number such that |x|lt1, then (1+x)^(n)=1+nx+(n(n-1)x^(2))/(2!)+(n(n-1)(n-2))/(3!).x^(3)+ . . . This can be used to find the sm of different series. Q. The sum of the series 1+(1)/(3^(2))+(1*4)/(1*2)*(1)/(3^(4))+(1*4*7)/(1*2*3)*(1)/(3^(6))+ . . . . is

Expand of the expression : (1-2x)^5

Find the sum of the last 30 coefficients in the expansion of (1+x)^(59), when expanded in ascending powers of x .