rewrite the series in sigma notation 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024

Answer 1

notice your numbers are simply powers of 2, with the exponent at 0 for
n = 1

∑ 2^(n-1) for n = 1 to 11

Answer 2

I think I'd prefer

10
∑ 2^n
n=0