Find the coefficient of - x100 in the expansion of 3-5x1-x2

Given expression can be written as #160; (3 5x)(1 x)^ 2= [1+2x+( 2)( 2 1)x^22!.....+( 2)( 2 1) #160; . .( 2 98)x^9999!+( 2)( 2 1) . . .( 2 99)x^100 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Middle Terms

Find the coef...

Question

Find the coefficient of :
$x^{100}$ in the expansion of $\frac{3 - 5 x}{(1 - x)^{2}}$

Open in App

Solution

Given expression can be written as

$(3 - 5 x) (1 - x)^{- 2} =$
$[1 + 2 x + (- 2) (- 2 - 1) \frac{x^{2}}{2!} . . . . . + (- 2) (- 2 - 1) . . (- 2 - 98) \frac{x^{99}}{99!} + (- 2) (- 2 - 1) . . . (- 2 - 99) \frac{x^{100}}{100!}]$

coefficient of $x^{100}$
$= 3. \frac{101!}{100!} - 5. \frac{100!}{99!} = 303 - 500 = - 197$

Suggest Corrections

Similar questions

The coefficient of $x^{9}$ in the expansion of $1 + x) ((1 + x^{2})$ $(1 + x^{3})$ $\dots$ $(1 + x^{100})$ is

Q. Find the coefficient of

x

in the expansion of

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

Q. Find the coefficient of

x^{r}

in the expansion of

\frac{(1 - x)^{2}}{(1 + x)^{3}}

Q. The coefficient of

x^{50}

in the expansion of

\frac{(3 - 5 x)}{(1 - x)^{2}}

equals

Q. What is the coefficient of

x^{2}

in the expansion of

(3 x^{2} - \frac{1}{5} x + 1) (5 x + \frac{1}{3})

Join BYJU'S Learning Program

Find the coefficient of :x100 in the expansion of 3−5x(1−x)2

Given expression can be written as (3−5x)(1−x)−2=[1+2x+(−2)(−2−1)x22!.....+(−2)(−2−1)..(−2−98)x9999!+(−2)(−2−1)...(−2−99)x100100!]coefficient of x100=3.101!100!−5.100!99!=303−500=−197

Find the coefficient of :
$x^{100}$ in the expansion of $\frac{3 - 5 x}{(1 - x)^{2}}$