Binomial Theorem And Its Simple Applications Question 44
Question: The coefficient of $ x^{n} $ in the expansion of $ {{(1-9x+20x^{2})}^{-1}} $ is
Options:
A) $ 5^{n}-4^{n} $
B) $ {5^{n+1}}-{4^{n+1}} $
C) $ {5^{n-1}}-{4^{n-1}} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ {{(1-9x+20x^{2})}^{-1}}={{[(1-4x)(1-5x)]}^{-1}} $
$ =\frac{1}{x}[ \frac{(1-4x)-(1-5x)}{(1-4x).(1-5x)} ]=\frac{1}{x}[{{(1-5x)}^{-1}}-{{(1-4x)}^{-1}}] $
$ =\frac{1}{5}[(5-4)x+(5^{2}-4^{2})x^{2}+(5^{3}-4^{3})x^{3} $
$ +……+(5^{n}-4^{n})x^{n}+……] $
$ \therefore $ coeff. of $ x^{n}={5^{n+1}}-{4^{n+1}} $
BETA
