Binomial Theorem And Its Simple Applications Question 170
Question: The fractional part of $ 2^{4n}/15 $ is $ (n\in N) $
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{1}{x} )}^{r}}{{=}^{m}}C_{r}{x^{2m-3r}}=\frac{{{(15+1)}^{n}}}{15} $
$ =\frac{{{(}^{n}}C_015^{n}{{+}^{n}}C_1{15^{n-1}}+…{{+}^{n}}{C_{n-1}}15{{+}^{n}}C_{n})}{15} $ = integer $ +\frac{1}{15} $
Hence, the fractional part of $ \frac{2^{4n}}{15} $ is $ \frac{1}{15} $
BETA
