April 06, 2016
9.5 Infinite Geometric Series
What does divergent
mean in a mathematical
series ?
In a series, the sum
grows infinitely...without
boundaries.
April 06, 2016
April 06, 2016
9.5 day 2 Infinite Geometric Series
If you added every number in an
infinite geometric series, what happens?
The sum increases infinitely. Divergent!
The sum gets closer to 13.5.
convergent!
The sum gets closer to 17.8.
convergent!
The sum increases infinitely. Divergent!
The sum gets closer to 2/3.
convergent!
The sum is 0 or 3.
Divergent!
convergent!
convergent!
April 06, 2016
The terms of a geometric series grow rapidly when the
common ratio is greater that 1. Likewise, they diminish
rapidly when the common ratio is between 0 and 1. In fact,
they diminish so rapidly that an infinite geometric series has
a finite sum.
Can only use the formula
for a convergent series...
grows rapidly to
infinity(+ or -)
rapidly converges
to a sum
grows rapidly to
infinity(+ or -)
April 06, 2016
Convergent or Divergent?
You can't type in the infinity symbol on your calculator.
100 is sufficiently large to find the sum of the series.
If you encounter an error, use a smaller upper limit.
Use the formula
to add the series
OR...
summation notation
OR...
April 06, 2016
Does the series diverge or converge?
April 06, 2016
Does the series converge or diverge? If if
converges, what is the sum?
1.
2.
divergent
convergent
3.
4.
convergent
divergent
April 06, 2016
5.
6.
convergent
convergent
April 06, 2016
Suppose a dropped ball bounces back to 4/5 of its orginial
7. height. A ball falls from a height of 5 feet and keeps
bouncing until someone picks it up. Estimate the total vertical
distance the ball travels if no one picks it up.
convergent
but actually not - don't forget
the height it rises before it falls!
April 06, 2016
HW p.599; 17 - 31 all, 41 - 45 all
April 06, 2016
HW p.599; 17 - 31 all, 41 - 45 all