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.

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11.4 – Infinite Geometric Series. Sum of an Infinite Geometric Series.

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Presentation transcript:

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 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!

Ex 1 – find the sum of: r=1/2 a … r=0.01 b … Changing repeating decimals to fractions…

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

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

geo

HW – Infinite Geo Series and Sigma Notation wksht Out – write 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!!