Fractional part of the number 4 2022 15 is equal to [2023]

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Solution

Q.
Fractional part of the number $\frac{4^{2022}}{15}$ is equal to [2023]

1 $\frac{1}{15}$

2 $\frac{4}{15}$

3 $\frac{14}{15}$

4 $\frac{8}{15}$

Ans.
(1)

$We have,$ ${\frac{4^{2022}}{15}}$ $= {\frac{{(4^{2})}^{1011}}{15}}$ $= {\frac{{(1 + 15)}^{1011}}{15}}$

$= {\frac{1}{15} + \frac{15^{1010}}{15} + \dots}$ $= {\frac{1}{15} + 0 + \dots}$ $= {\frac{1}{15}}$

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