Download presentation

1
**12.3 Infinite Sequences and Series**

2
**Infinite sequence – a sequence that has infinitely many terms.**

Limits can be used to determine if a sequence approaches a value.

3
When any positive power of n appears only in the denominator of a fraction and n approaches infinity, the limit equals zero.

4
**Ex 1 Estimate the limit of**

5
**For sequences with more complicated general forms**

For sequences with more complicated general forms. Applications of the following limit theorems can make the limit easier to find.

6
Ex 2 Find the limit

7
Ex 3 find the limit

8
**Limits don’t exist for all infinite sequences**

Limits don’t exist for all infinite sequences. If the absolute value of a sequence becomes arbitrarily great or if the terms don’t approach a value the sequence has no limit. EX 4

9
Ex 5

10
**When n is even, (-1)n = 1 and when n is odd, (-1)n = -1**

When n is even, (-1)n = 1 and when n is odd, (-1)n = -1. Therefore the sequence would have no limit.

11
Sum of an Infinite Series – if Sn is the sum of the first n terms and S is a number such that S – Sn approaches zero as n increases without bound, then the sum of the infinite series is S.

12
**Sum of an Infinite Geometric Series**

13
Ex 6 find the sum of …

14
Ex 7 write …as a fraction

Similar presentations

Presentation is loading. Please wait....

OK

What is the sum of the following infinite series 1+x+x2+x3+…xn… where 0

What is the sum of the following infinite series 1+x+x2+x3+…xn… where 0

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on service oriented architecture pdf Ppt on low level language Ppt on standing order act 1946 Ppt on biodiversity and its conservation Ppt on mechanical power transmission system Ppt on natural and artificial satellites images Oral cavity anatomy and physiology ppt on cells Ppt on condition based maintenance management Ppt on psu in india Ppt on social networking sites in india