1. 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!

2. Notes! Formula for the sum of a FINITE geometric If r is a fraction, becomes smaller as n becomes larger. When gets close to zero, then the formula for becomes: If r is not between 1 and -1, then there is no sum!

3. Ex 1 – find the sum of: r=1/2 a. 20+10+5+… r=0.01 b. 0.81+0.0081+0.000081+… Changing repeating decimals to fractions…

4. Sigma Notation The Greek letter,, is used to indicate sums First position # last position # rule Ex 2 – expand:

5. Ex 3 – find the sum: Arith or Geo? Arith Ex 4 – write the series using sigma notation: Find the rule first Arith

6. geo

7. HW – Infinite Geo Series and Sigma Notation wksht Out – write 4+20+100+500+2500+12500 in sigma notation Summary – You can’t find the sum of an infinite sequence when r isn’t a fraction because… Don’t forget about POW!!