Binomial Theorem And Its Simple Applications Question 57
Question: If $ f(x)=1-x+x^{2}-x^{3}+…-x^{15}+x^{16}-x^{17} $ then the coefficient of $ x^{2} $ in f(x-1) is
Options:
A) 826
B) 816
C) 822
D) none of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ f(x)=1-x+x^{2}-x^{3}+…-x^{15}+x^{16}-x^{17}=\frac{1-x^{18}}{1+x} $
$ \Rightarrow f(x-1)=\frac{1-{{(x-1)}^{18}}}{x} $ Therefore, required coefficient of $ x^{2} $ is equal to coefficient of $ x^{3} $ in $ 1-{{(x-1)}^{18,}} $ which is given by $ ^{18}C_3=816 $ .
BETA
