Infinite GP’s

Sum of an Infinte GP: the sum of a infinite sequence can converge or diverge Converge: A sequence that converges has a limit it approaches.  Diverge: A sequence that diverges either has no limit or approaches infinity.

Common Ratio The absolute value of the common ratio must be less than 1 If we remember absolute values then what range must r be in? What happens if r is greater than 1 or less than -1?

Example Figure out if each sequence is converging or diverging:

Example For what values of this does the series converge?

Example Find the first 3 terms of the infinite GP: Sum=1 and a=1/2

Example Find the sum of an infinite GP if the sum of the first two terms is 80 and the third term is 4.

Group Problem Find all values of x which work for the given infinite GP Sum