A) \[{{5}^{n}}-{{4}^{n}}\]
B) \[{{5}^{n+1}}-{{4}^{n+1}}\]
C) \[{{5}^{n-1}}-{{4}^{n-1}}\]
D) None of these
Correct Answer: B
Solution :
[b] \[{{(1-9x+20{{x}^{2}})}^{-1}}={{[(1-4x)(1-5x)]}^{-1}}\] \[=\frac{1}{x}\left[ \frac{(1-4x)-(1-5x)}{(1-4x).(1-5x)} \right]=\frac{1}{x}[{{(1-5x)}^{-1}}-{{(1-4x)}^{-1}}]\] \[=\frac{1}{5}[(5-4)x+({{5}^{2}}-{{4}^{2}}){{x}^{2}}+({{5}^{3}}-{{4}^{3}}){{x}^{3}}\] \[+......+({{5}^{n}}-{{4}^{n}}){{x}^{n}}+......]\] \[\therefore \] coeff. of \[{{x}^{n}}={{5}^{n+1}}-{{4}^{n+1}}\]
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