Presentation is loading. Please wait.

Presentation is loading. Please wait.

12.3 Infinite Sequences and Series. Infinite sequence – a sequence that has infinitely many terms. Infinite sequence – a sequence that has infinitely.

Similar presentations


Presentation on theme: "12.3 Infinite Sequences and Series. Infinite sequence – a sequence that has infinitely many terms. Infinite sequence – a sequence that has infinitely."— Presentation transcript:

1 12.3 Infinite Sequences and Series

2 Infinite sequence – a sequence that has infinitely many terms. Infinite sequence – a sequence that has infinitely many terms. Limits can be used to determine if a sequence approaches a value. 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. 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 dont exist for all infinite sequences. If the absolute value of a sequence becomes arbitrarily great or if the terms dont approach a value the sequence has no limit. EX 4 EX 4

9 Ex 5

10 When n is even, (-1) n = 1 and when n is odd, (-1) n = -1. Therefore the sequence would have no limit. 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 S n is the sum of the first n terms and S is a number such that S – S n approaches zero as n increases without bound, then the sum of the infinite series is S. Sum of an Infinite Series – if S n is the sum of the first n terms and S is a number such that S – S n 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


Download ppt "12.3 Infinite Sequences and Series. Infinite sequence – a sequence that has infinitely many terms. Infinite sequence – a sequence that has infinitely."

Similar presentations


Ads by Google