Infinite Series Lesson 8.5

Infinite series To find limits, we sometimes use partial sums. If Then In other words, try to find a finite limit to an infinite series.

Theorem Series, g 1 + g 1 r + g 1 r 2 + … + g 1 r n-1, with g 1 ≠ 0 A. if |r| < 1, series converges and B. if |r|≥ 1, the series diverges.

Example 1 Consider Write the first 3 terms of the sequence of partial sums of this series. 1/3 4/9 13/27

Example 1 continued… Write an explicit formula for the nth partial sum. Does the series converge? If so, what is its sum? Yes – to 1/2

Example 2 A ball dropped 60 feet rebounds on each bounce to ¾ of the distance from which it fell. How far will it travel before coming to a rest. G1 = 60 R = 3/4

Example 3 State whether convergent or divergent If convergent, give its sum G1 = 325 R = 1/10

Homework Pages – 14 Skip 13b.