1.4 Infinite Geometric Series

Learning Objective: to explore what happens when a geometric series is infinite and to express it using sigma notation.

Warm-up (IN)

HW/INB Check!

When you’re finished…grab a quiz!

Notes!

Formula for the sum of a FINITE geometric

1 1

1

n

n

a rS

r

If r is a fraction ,

becomes smaller as n becomes larger.

When gets close to zero, then the formula for becomes:

1 1r nr

nr

1

1

aS

r

If r is not between 1 and -1, then there is no sum!

Ex 1 – find the sum of:

r=1/2

1

1

aS

r

201

12

20

1

2

40

a. 20+10+5+…

r=0.01

1

1

aS

r

.81

1 .01 .81

.99

b. 0.81+0.0081+0.000081+…

81

99 9

11

Changing repeating decimals to fractions…

81.0 ...818181.0 81. 0081. 000081.

Sigma Notation

The Greek letter, , is used to indicate sums

10

1

2n

n

First position #

last position #

rule

Ex 2 – expand:10

1

a. 2n

n 2 4 6 8 10 12 14 16 18 20

4

1

1

b. 3 2k

k

3 6 12

Ex 3 – find the sum:

6

1

3 1n

n

Arith or Geo?

Arith

1

2n

n

a a nS

2 17

6

257

Ex 4 – write the series using sigma notation:

a. 2+6+10+14+18+22+26+30 Find the rule first

1 1na a n d Arith

na 2 1n 4

na 4n2 4

na 4n 2

1n

8

4 2n

24

b. 2+6+18+54+162 geo

11n

na a r

na 2 31n

1n

5

12 3

n

HW – Infinite Geo Series and Sigma Notation wksht

Out – write 4+20+100+500+2500+12500 in sigma notationSummary – You can’t find the sum of an infinite sequence when r isn’t a fraction because…

Don’t forget about POW!!