Question

Find the sum. $$\sum_{i=1}^{4} \frac{1}{2^{i}}$$

   Find the sum.
$$\sum_{i=1}^{4} \frac{1}{2^{i}}$$

Contemporary Precalculus

Contemporary Precalculus

Thomas W.… 5th Edition

Chapter 12, Problem 46

Instant Answer

Solved by Expert Amy Jiang

07/17/2020

Step 1

This is a finite geometric series with the first term $a = \frac{1}{2}$, the common ratio $r = \frac{1}{2}$, and the number of terms $n = 4$. Show more…

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Find the sum. $$\sum_{i=1}^{4} \frac{1}{2^{i}}$$

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Key Concepts

Geometric Series

A geometric series is a sequence of numbers where each term after the first is found by multiplying the previous term by a common ratio. This concept underlies many problems in mathematics where understanding the behavior of sequences with multiplicative factors is essential.

Finite Summation

Finite summation refers to the process of adding a specific, limited number of terms together. It is used to represent and compute the total of a sequence of terms, often expressed using summation notation for clarity and efficiency.

Exponential Expressions

Exponential expressions involve raising a constant base to a variable exponent, a concept that is central to many areas of mathematics. They are particularly important in the context of geometric series, where each term is typically expressed as an exponentiation of the common ratio.

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