find the sum to 10th term of the series:1/2+7/4+23/8+63/16+.....

Answer 1

This sequence of terms appears to be a_n = (n*2ⁿ - 1)/2ⁿ = n - (1/2)ⁿ

The 2 terms can be summed separately:

The sum of n is 10*11/2 = 55

The sum of the fraction is 1 - (1/2)¹⁰

I will leave the nuisance arithmetic to you!