Question

Evaluate each series. $$\sum_{i=1}^{5}(-1)^{i+1} \cdot(i)$$

   Evaluate each series.
$$\sum_{i=1}^{5}(-1)^{i+1} \cdot(i)$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Sherri Messersmith 2nd Edition

Chapter 15, Problem 47

Instant Answer

Solved by Expert Amy Jiang

06/26/2020

Step 1

Step 1: We start by writing out the terms of the series: $$(-1)^{1+1} \cdot(1), (-1)^{2+1} \cdot(2), (-1)^{3+1} \cdot(3), (-1)^{4+1} \cdot(4), (-1)^{5+1} \cdot(5)$$ Show more…

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Evaluate each series. $$\sum_{i=1}^{5}(-1)^{i+1} \cdot(i)$$

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Key Concepts

Reciprocal Function

The reciprocal of a number is given by one divided by that number. Understanding reciprocal functions is important when evaluating expressions where terms are of the form (variable + constant) raised to a power that results in an inversion, which affects the strategy for simplifying or summing the series.

Finite Series

A finite series is the sum of a finite number of terms in a sequence. Working with finite series involves computing each term explicitly and summing them, which is a foundational technique in algebra and discrete mathematics.

Summation Notation

Summation notation is a concise way of writing the sum of a sequence of terms. It uses the sigma symbol (?) along with an index that runs over a set of discrete values, helping to clearly define both the structure of the sequence and the operation of addition over its terms.

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