Question Detail

MTH 101 MTH 101 Past Questions Objective Question
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Question

Which formula holds for \(\sum_{k=1}^n 2^k\) for all \(n \geq 1\)
Options
A \(\sum_{k=1}^n 2^k = 2^n - 1\)
B \(\sum_{k=1}^n 2^k = 2^{n+1} - 2\)
Correct Answer
C \(\sum_{k=1}^n 2^k = n2^n - 1\)
D \(\sum_{k=1}^n 2^k = 2^n\)
Correct Answer

Option B is the correct answer.

Detailed Explanation

Geometric series: first term (a=2), ratio (r=2), (n) terms. Sum = (2(2^n-1)/(2-1) = 2^{n+1} - 2).

Hint

Use the formula for sum of geometric series: \(S_n = a(r^n-1)/(r-1)\).

Question Info

Course: MTH 101
Topic: MTH 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 589 of 696
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