Binomial Theorem And Its Simple Applications Question 72
Question: $ ( \begin{matrix} n \\ 0 \\ \end{matrix} )+2,( \begin{matrix} n \\ 1 \\ \end{matrix} )+2^{2}( \begin{matrix} n \\ 2 \\ \end{matrix} )+…..+2^{n}( \begin{matrix} n \\ n \\ \end{matrix} ) $ is equal to
[AMU 2000]
Options:
A) $ 2^{n} $
B) 0
C) $ 3^{n} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- $ {{(1+x)}^{n}}={}^{n}C_0+x.{}^{n}C_1+x^{2}.{}^{n}C_2+….+x^{n}.{}^{n}C_{n} $ Put x = 2
therefore $ 3^{n}={}^{n}C_0+2.{}^{n}C_1+2^{2}.{}^{n}C_2+2^{3}.{}^{n}C_3+….+2^{n}{{.}^{n}}C_{n} $ .
BETA
