Question

If $\left\{x\right\}$ denotes the fractional part of $x$ then $\left\{\frac{3^{2n}}{8}\right\}$,$nϵN$,is

• A. $\frac{3}{8}$
• B. $\frac{7}{8}$
• C. $\frac{1}{8}$
• D. none of these

Answer 1

The correct option is C $\frac{1}{8}$

Given, $\frac{9^n}{8}$
$=\frac{(1+8{)}^n}{8}$
$=\frac{1+8k}{8}$ where $kϵN$.
$=\frac{1}{8}+k$.
Hence fractional part is $\frac{1}{8}$.