Sequences and Series Day 2&3

Happy Monday 1-26-15

Warm-UP

1)What is the 50th term if we know the sequence is defined as ?

2) Find the first 5 terms of the sequence knowing

Question on the homework?

Sequences : Partial Sums

In further math courses we become more interested in the sum of these sequences.

Definition Partial sums: for sequence the partial sums are

All the way to

Sequences : Partial Sums

is the first partial sum is the second partial sum and so on… is the nth partial sum

Note : the sequence is call the sequence of partial sums.

Sequences : Partial Sums

EX: Find the first 4 partial sums and the nth partial sum of the sequence given by • Good idea to find the first 4 terms of the

sequence then the sums.

• • You find

and

given

You try

Find the first 4 partial sums of

Answers

Homework

Page 826: # 25-30

Good afternoon Happy Tuesday!

1-27-15

Warm-UP

1) Find the first 4 partials sums of the sequence defined by:

2) Find the firs 4 pratial sums of the sequence defined by

Questions on the Homework?

Sigma Notation

• Given a sequence we can write the sum of the first n terms using summation notation or (aka) sigma notation. It is derived from the Greek letter

( capital sigma, corresponding to our S for “sum”) Used as follows:

Sigma notation

• The left side of the expression is read “ The sum of from ”

• The letter k is called the index of summation, or summation variable.

• The idea is to replace k in the expression after the sigma by the integers 1,2,3…, n and add the resulting expressions, arriving at the right side of the equation.

Example

Find the sum:

Well•

Put in sigma notation:

Write each sum using sigma notation:

Each integer is being cubed the lowest is integer 1 the integer is 7.So

Good afternoon Happy Wednesday!

Sigma notation

∑𝑘=1

𝑛

𝑎𝑘=𝑎1+𝑎2+𝑎3+…+𝑎𝑛

3 Properties

Let be sequences. The for every positive integer n and any real number c, the following properties hold.

Practice Problems

Let’s do some practice!

Front page 34-54 even

Good afternoon Happy Thursday!!!!

Answers to 34-54

34) 3036) 038) 9040) 3442) 44) 46)

48)

50)

52)

Answers to 5454)

Homework answers 33-53

33)35)37) 39)41)43)

45) 47)

49)

51)

53)

Tonight

Continue working on the practice for quiz.

Answers will be posted tonight along with all of the slide from the last week.

Practice

Find each sum:

Write in sigma notation: 4)

Homework due on Friday (1-30-15)

Homework front page : #’s 25-28 , 33-53 odd.

Quiz Friday