Express each sum using summation notation. 1-(1)/(3)+(1)/(9)-(1)/(27)+⋯+(-1)^6((1)/(3^6))

Name: Problem 63, Chapter 9: College Algebra
Uploaded: 2020-05-14T02:58:19-08:00
Duration: 1 min 48 s
Channel: Julie Silva
Description: Express each sum using summation notation. 1-(1)/(3)+(1)/(9)-(1)/(27)+⋯+(-1)^6((1)/(3^6))

step 1 We're being asked to write our sum using summation notation. So to do this, let's look at our ve

Express each sum using summation notation....

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Summation Notation

Summation notation is a compact way to represent the sum of a sequence by using the sigma symbol (?). It allows you to define the range of indices and provide a general expression for each term, making it easier to work with series and perform operations such as differentiation or integration on them.

Finite Series

A finite series is a sum that includes a specific, countable number of terms. Representing finite series with summation notation involves specifying both the starting and ending indices, which clearly communicates the complete set of terms being added.

Geometric Series

A geometric series is a sequence in which each term is obtained by multiplying the previous term by a fixed factor known as the common ratio. When expressed in summation notation, the general term often involves an exponent that reflects the position of each term in the series.

Alternating Series

An alternating series is one in which the sign of the terms alternates between positive and negative. This pattern is typically achieved by including a factor such as (-1) raised to an index power in the general term, which systematically changes the sign of each successive term.

Transcript

Please give Ace some feedback