Question

evaluate the series 1+2+4+8+...+a10

Answer 1

Looks like the sum is
\[\sum_{n=0}^{10}2^{n}=2^0+2^1+2^2+\cdots+2^8+2^9+2^{10}\]

Answer 2

Then simply use the formula to find the sum:
\[S_n=\sum_{n=0}^{k-1} ar^{n}=\frac{a(1-r^k)}{1-r}\]