Upper bound for sum of powers of 2 from 1 to $\log n$ where powers are multiplied by 2 each time?
I'm trying to find the upper bound for the following series
$$s(n) = 2^1 + 2^2 + 2^4 + 2^8 + 2^{16} + 2^{32} + \dots + 2^{\log n}.$$
From the series, it is clear that the exponent of the $i$th term is obtained by multiplying the exponent of the $(i-1)$th term exponent.
It is clear that the series is not a Geometric Progression. Can someone suggest any other hints to solve the sequence?