Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2015 / Paper 1 / 10

Pair the first and last terms of the arithmetic series. There are $500$ pairs, each summing to $1001$, so

The finite geometric series has eleven terms, from $2^1$ through $2^{11}$. With common ratio $2$,Counting the powers explicitly avoids omitting the final $2048$ term.