Question

The sum to n terms of the series \frac12+\frac34+\frac78+(15)/(16)+⋯ is

• A. \(n-1-2^{-n}\)
• B. \(1\)
• C. \(n-1+2^{-n}\)
• D. 1+2⁻n

Hint:

Convert series into a simpler form using geometric sums.

Answer 1

The Correct Option is A

Each term is: 1-(1)/(2ᵏ) Sum: Sₙ=n-(1+\frac12+⋯+(1)/(2ⁿ)) =n-(2-2⁻n) =n-2+2⁻n