Question

If {x} denotes the fractional part of x, then `{(3^(2n))/8},n in N ,` is
A. `(3)/(8) `
B. `(7)/(8)`
C. `(1)/(6)`
D. none of these

Answer 1

Correct Answer - c
We have,
`3^(2n) = (1 + 8)^(n)`
`rArr 3^(2n) = ""^(n)C_(0) + ""^(n)C_(1) xx 8 + ""^(n)C_(2) xx 8^(2) + …+ ""^(n)C_(n) xx 8^(n)`
`rArr (3^(2n))/(8) = ( ""^(n)C_(1) + ""^(n)C_(2) xx8 + ...+ ""^(n)C_(n) + 8^(n -1)) + (1)/(8)`
`rArr (3^(2n))/(8) = A` positive integer ` + (1)/(8)`
`rArr {(3^(2n))/(8)} = (1)/(8)`.