Binomial Theorem And Its Simple Applications Question 207
Question: The fractional part of $ \frac{2^{4n}}{15} $ is
Options:
A) $ \frac{1}{15} $
B) $ \frac{2}{15} $
C) $ \frac{4}{15} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] $ \frac{2^{4n}}{15}=\frac{16^{n}}{15}=\frac{{{(1+15)}^{n}}}{15} $
$ =\frac{1+{{,}^{n}}C_1,15+{{,}^{n}}C_2,15^{2}+….+{{,}^{n}}C_{n}15^{n}}{15} $
$ =\frac{1+15,k}{15}, $ where $ k\in N,=\frac{1}{15}+k $
$ \therefore $ Fractional part of $ \frac{2^{4n}}{15} $ is $ \frac{1}{15} $
BETA
