 ## Tutoring on Infinite Series

Learning Objectives:

#### Understand the application of Infinite Series

Math Tutoring on Infinite Series

A sequence is an ordered list of terms or elements. There are two types of sequences, a finite sequence, and an infinite sequence. An infinite sequence is the one which continues on forever. Infinite series is defined as the sum of the terms of an infinite sequence. Given an infinite sequence of numbers {aᵣ}, a series is informally the result of adding all those terms together: a1 + a2 + a3 + · · ·. An arithmetic series is the sum of an arithmetic sequence, a sequence with a common difference between each two consecutive terms. If a series has a limit, and the limit exists, the series converges. If a series does not have a limit, or the limit is infinity, then the series is divergent.  Conversely, a series is divergent if the sequence of partial sums is divergent. Convergence and divergence are unaffected by deleting a finite number of terms from the beginning.  An infinite series of numbers is said to converge absolutely if the sum of the absolute value of the summand is finite. Summing or adding the terms of a geometric sequence creates what is called a geometric series.

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Hook Questions:

1. What is the partial sum?

2. What is the definition of infinite sequence?

3. Can an infinite arithmetic series ever converge?

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