Question

Find the sum of each sequence. $$\sum_{i=1}^{\infty} k^{3}$$

   Find the sum of each sequence.
$$\sum_{i=1}^{\infty} k^{3}$$

College Algebra

College Algebra

Michael Sullivan 9th Edition

Chapter 9, Problem 79

Instant Answer

Solved by Expert Yujie Wang

09/18/2021

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This means that every term in the sequence is the same, and equal to $k^{3}$. Show more…

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Find the sum of each sequence. $$\sum_{i=1}^{\infty} k^{3}$$

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Key Concepts

Infinite Series

An infinite series is the sum of the terms of an infinite sequence. It is evaluated by considering the sequence of partial sums. The study of infinite series involves determining whether these partial sums converge to a finite limit or diverge, meaning that they do not approach a fixed number.

Convergence and Divergence

Convergence refers to the property where the sequence of partial sums of a series approaches a specific finite value. Divergence means that the partial sums do not settle to a finite limit, instead possibly growing without bound or oscillating. Determining convergence is crucial for knowing if an infinite series has a meaningful sum.

Test for Divergence

The term test for divergence is a basic criterion used to assess whether an infinite series converges. It states that if the limit of the sequence of terms does not approach zero as the index goes to infinity, then the series must diverge. This test is fundamental in series analysis, especially for series with terms that grow rapidly, such as polynomial terms.

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