First slide

Binomial theorem for positive integral Index

Question

The fractional part of $2^{4 n} / 15 is (n \in N)$

Moderate

A

$\frac{1}{15}$
B

$\frac{2}{15}$
C

$\frac{4}{15}$
D

$\frac{3}{15}$

Solution

$\begin{matrix} \frac{2^{4 n}}{15} = \frac{(15 + 1)^{n}}{15} \\ = \frac{(^{n} C_{0} 15^{n} +^{n} C_{1} 15^{n - 1} + \dots +^{n} C_{n - 1} 15 +^{n} C_{n})}{15} \\ = Integer + \frac{1}{15} \end{matrix}$
Hence, the fractional part of $\frac{2^{4 n}}{15} is \frac{1}{15}$ .

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App