Consider the following sequence 1,1,(3)/(4) ,(4)/(8) find the nth term such that n > 0

Question

Consider the following sequence


`1,1,(3)/(4) ,(4)/(8)`
find the nth term such that n > 0

Answer 1

9514 1404 393

Answer:

2n/2^n

Explanation:

It appears that the terms are ...

`(1)/(1),\ (2)/(2),\ (3)/(4),\ (4)/(8),\ \dots`

That is, the numerator is counting numbers, and the denominator is powers of 2.

`f[n]=(n)/(2^((n-1)))\quad\text{or}\quad f[n]=2n\cdot2^(-n)`