Question Detail
Question
Which formula holds for \(\sum_{k=1}^n 2^k\) for all \( n \geq 1 \)
Correct Answer
Option B is the correct answer.
Detailed Explanation
The sum of a geometric series: a + ar + ar² + ... + ar^(n-1) = a(r^n - 1)/(r-1). Here, the series is 2¹ + 2² + ... + 2^n = 2(2^n - 1)/(2-1) = 2(2^n - 1) = 2^(n+1) - 2.
Hint
This is a geometric series with first term a=2, common ratio r=2, and n terms.