In Exercises 29–42, find each indicated sum. 4Σi=1 (−1/2)^i

Key Concepts

Summation Notation

Summation notation, represented by the sigma symbol (Σ), is a concise way to express the sum of a sequence of terms. The notation includes an index of summation, which indicates the starting and ending values for the variable, and a function of that variable. In this case, the sum is calculated from i=1 to i=4, meaning we will evaluate the expression for each integer value of i within that range.

Geometric Series

A geometric series is a series of terms where each term after the first is found by multiplying the previous term by a constant called the common ratio. The series can be finite or infinite, and its sum can be calculated using specific formulas. In this problem, the terms involve powers of (-1/2), which indicates a geometric series with a common ratio of -1/2.

Evaluating Powers

Evaluating powers involves calculating the result of raising a base to an exponent. In this context, we need to compute (-1/2)^i for i values from 1 to 4. Understanding how to compute these powers is essential for finding the individual terms of the series before summing them up to get the final result.