Sec 2.4 Pr 4 **Problem 4: Use the Principle of Mathematical Induction (PMI) to prove the following statement for all natural numbers \( n \).****(c)** \( \sum_{i=1}^{n} 2^i = 2^{n+1} - 2 \)In this problem, you are asked to use the Principle of Mathematical Induction to prove that the sum of the series \( \sum_{i=1}^{n} 2^i \) is equal to \( 2^{n+1} - 2 \) for all natural numbers \( n \).*Steps Involved in Mathematical Induction:*1. **Base Case**: Verify the statement for the initial value, typically \( n=1 \).2. **Inductive Step**: Assume the statement holds for \( n = k \), and then prove it holds for \( n = k+1 \).The given series and expression involve exponential growth, and confirming this identity through PMI solidifies your understanding of series summation and exponentiation properties in algebra.

Name: Sec 2.4 Pr 4 **Problem 4: Use the Principle of Mathematical Induction
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: Sec 2.4 Pr 4 **Problem 4: Use the Principle of Mathematical Induction (PMI) to prove the following statement for all natural numbers \( n \).****(c)** \( \sum_{i=1}^{n} 2^i = 2^{n+1} - 2 \)In this problem, you are asked to use the Principle of Mathem