So I am given a sequence where the terms $T(n)$ are: $1, 4, 11, 26, 57, 120$ and so on.
Each term is generated by the sum $\sum\limits_{n=1}^k(2^n-1)$
I am being asked to express this sum above in terms of $n$ without the sigma notation, such that I can generate any term $T(n)$ by plugging in a value of $n$ where $n$ belongs to the integers.
I've been stuck in this for a while and I don't know what to do! I would really appreciate some help and I'm slightly short on time. Thanks for the help!