Sum of Series to Infinity (I)
Use this exercise to explore the sum of the series shown below.
(The sum to the first n terms has been provided without proof, you may want to work out and verify yourself)
1. Move the slider to n = 20, and state the sum of the first 20 terms of the series.
2. Change the maximum number of terms to sum from 20 to 1000
3. Now find the sum of the series to 100 terms, then to 500 terms, and then to 1000 terms.
4. What do you notice about the sum of the series as n increases from 20 to 1000.
5. What can you conclude about sum of the series if n is an infinitely large number?
(ie sum the series to infinity)