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The fractional part of 2^(4n)//15 i s(n ...

The fractional part of `2^(4n)//15 i s(n in N)` `1/(15)` b. `2/(15)` c. `4/(15)` d. none of these

A

`1/15`

B

`2/15`

C

`4/15`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(2^(4n))/(15)=((15+1)^(n))/(15)`
`=(.^(n)(C_(0)15^(n)+.^(n)C_(1)15^(n-1)+"......"+.^(n)C_(n-1)15+.^(n)C_(n)))/(15)`
`= "Integer" + 1/15`
Hence, the fractional part of `(2^(4n))/(15)` is `(1)/(15)`.
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