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 ...

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Byju's Answer

Standard XII

Mathematics

Middle Terms

Find the coef...

Question

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

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

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