Question:
If $\{p\}$ denotes the fractional part of the number $p$, then $\left\{\frac{3^{200}}{8}\right\}$, is equal to :
Correct Option: , 4
Solution:
$\frac{3^{200}}{8}=\frac{1}{8}\left(9^{100}\right)$
$=\frac{1}{8}(1+8)^{100}=\frac{1}{8}\left[1+n \cdot 8+\frac{n(n+1)}{2} \cdot 8^{2}+\ldots .\right]$
$=\frac{1}{8}+$ Integer
$\therefore\left\{\frac{3^{200}}{8}\right\}=\left\{\frac{1}{8}+\right.$ integer $\}=\frac{1}{8}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.