A) \[n(n-1){{2}^{n-1}}\]
B) \[(n-1){{2}^{n-1}}\]
C) \[n(n-1){{2}^{n-2}}\]
D) \[n(n-1){{2}^{n}}\]
Correct Answer: C
Solution :
Given, \[f(x)=1+nx+\frac{n(n-1)}{2!}{{x}^{2}}\] \[+\frac{n(n-1)(n-2)}{3!}{{x}^{3}}+......+{{x}^{n}}\] \[\Rightarrow \] \[f(x)={{(1+x)}^{n}}\] \[\Rightarrow \] \[f'(x)=n{{(1+x)}^{n-1}}\] \[\Rightarrow \] \[f''(x)=n(n-1){{(1+x)}^{n-2}}\] \[\Rightarrow \] \[f''(1)=n(n-1){{2}^{n-2}}\]You need to login to perform this action.
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