This preview shows page 1. Sign up to view the full content.
Unformatted text preview: k k k 1 Telescoping Series Continued
We call a series telescoping when we find that all (most) of the middle terms cancel in the partial sum from n=1 to k. We can take the limit of the sum to find the value of the infinite series (just as we did in the previous example).
Most series do not behave this way, but it is helpful when we have a telescoping series so that we can find the true sum of the series rather than approximate the sum. Typically we can do a telescoping series when we can write the series in the form:
tn = An – Bn
Where An and Bn start to share indices at some point (that is n will become n+1 after one iteration of the index, n will become n+5 after 5 iterations of the index, and so on). Strategy For Telescoping Series
1. Write the expression of the series as a subtraction of 2 (or more) expressions. 2. Write the partial sums of Sk using the bounds of the summation. (Go far enough until you can see which ones cancel from both ends. 3. Simplify Sk and take the limit as k∞ so that you can ﬁnd the value of the infinite serie...
View Full Document
This note was uploaded on 02/07/2014 for the course MATH 1004 taught by Professor Mark during the Summer '00 term at Carleton CA.
- Summer '00
- Calculus, SmartPen Lectures, Lecture Notes, MATH1004, Kyle Harvey