Download presentation

Presentation is loading. Please wait.

1
**12.7 (Chapter 9) Special Sequences & Series**

2
Fibonacci Sequence: 1, 1, 3, 5, 8, 13, … Describes many patterns of numbers found in nature. a1 = 1 and a2 = 1 How do we arrive at the next term? It was used to investigate the reproductive habits of rabbits in ideal conditions in 1202.

3
An important series used to define the irrational number e, developed by Leonhard Euler. It can be expressed as the sum of the following infinite series:

4
**The binomial theorem can be used to derive the series for e**

The binomial theorem can be used to derive the series for e. Let k be any positive integer and apply the binomial theorem to:

5
**Then find the limit as k increases without bound.**

6
**The value of ex can be approximated using the following series known as the exponential series.**

7
Ex 1 Use the first five terms of the exponential series and a calculator to approximate the value of e0.65 to the nearest hundredth.

8
Trigonometric Series

9
**The two trig series are convergent for all values of x**

The two trig series are convergent for all values of x. By replacing x with any angle measure expressed in radians and carrying out the computations, approximate values of the trig functions can be found to any desired degree of accuracy.

10
**Ex 2 Use the first five terms of the trig series to find the value of**

11
Euler’s Formula

12
Therefore:

13
**Ex 3 Write in exponential form:**

14
Recall: There is no real number that is the logarithm of a negative number. You can use a special case of Euler’s Formula to find a complex number that is the natural logarithm of a negative number.

16
Ex 4 Evaluate: ln(-540) ln(-270)

Similar presentations

OK

STROUD Worked examples and exercises are in the text PROGRAMME 14 SERIES 2.

STROUD Worked examples and exercises are in the text PROGRAMME 14 SERIES 2.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on indian politics and culture Free ppt on physical features of india Ppt on high court of india Ppt on conservation of forest Ppt on waves tides and ocean currents for kids Ppt on different types of forests in world Ppt on product design and development Ppt on online examination system in core java Ppt on going places Ppt on personality test