If Sn = Σ 1+2+2^2+......+r terms / 2^r ; r=1,n, then Sn is equal to ​

Question

If \(S_n = \sum\limits_{r = 1}^{n} \frac{1 + 2+2^2+.....+ r\; terms}{2^r}\), then S_n is equal to

(a) 2ⁿ – (n + 1)

(b) 1 – 2^–n

(c) n –1 + 2^–n

(d) 2ⁿ –1

Answer 1

Correct option is (c) n –1 + 2^–n