If {p} denotes the fractional part of the number p,
Question:

If $\{p\}$ denotes the fractional part of the number $p$, then $\left\{\frac{3^{200}}{8}\right\}$, is equal to :

  1. (1) $\frac{5}{8}$

  2. (2) $\frac{7}{8}$

  3. (3) $\frac{3}{8}$

  4. (4) $\frac{1}{8}$


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 $\}=\frac{1}{8}$

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