### Problem Statement from the Image:**Write the first five terms of an infinite geometric series that converges to 2.**### Explanation for Educational Website:This is a mathematical problem that requires identifying the first five terms of an infinite geometric series, which is a sequence where each term is found by multiplying the previous one by a fixed, non-zero number called the common ratio. The series must also converge to a limit of 2.**Key Concepts:**1. **Infinite Geometric Series:** - A series of the form \( a + ar + ar^2 + ar^3 + \cdots \), where \( a \) is the first term and \( r \) is the common ratio. 2. **Convergence of Geometric Series:** - An infinite geometric series \( a + ar + ar^2 + ar^3 + \cdots \) converges if the absolute value of the common ratio \( |r| < 1 \). - The sum \( S \) of an infinite geometric series is given by \( S = \frac{a}{1 - r} \) where \( |r| < 1 \).### Solving the Problem:Given that the series converges to 2, we use the formula for the sum of an infinite geometric series to set up the equation:\[ S = \frac{a}{1 - r} = 2 \]Let's find an example:1. Choose the first term \( a \) and a common ratio \( r \) such that \( |r| < 1 \).2. Solve for the values of \( a \) and \( r \) under the condition that \( \frac{a}{1 - r} = 2 \).One potential solution is:- Let \( a = 1 \) and \( r = \frac{1}{2} \).Then the series is:\[ 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \cdots \]**First five terms of the series:**\[ 1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16} \]This series converges to 2 because:\[ \frac{1}{1 - \frac{1}{2

Name: ### Problem Statement from the Image:**Write the first five terms of
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: ### Problem Statement from the Image:**Write the first five terms of an infinite geometric series that converges to 2.**### Explanation for Educational Website:This is a mathematical problem that requires identifying the first five terms of an infin