Evaluate 7 sigma n=1 2 (-2) ^n-1

Okay I think you mean the sum of the first 7 terms of the geometric sequence:

a (n) = 2 (-2) ^ (n-1)

The sum of any geometric sequence is:

s (n) = a (1-r^n) / (1-r) in this case:

s (7) = 2 (1--2^7) / (1-7)

s (7) = - 43