Finding the value of a series
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We have seen how we can find the value of a series using a geometric series (it has
a nice closed formula). We will also take a look at another series that you can
find the value of the series.
Keep in mind: Finding the value of an infinite series is a very challenging problem.
We will only look at the following easier cases, as the you can spend an entire
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course on solving infinite series techniques.
Since most problems in engineering only require you to be correct within an
acceptable error, we will be learning how to calculate the error after stopping
at n terms. This way we will know if our error is acceptable when dealing with
an infinite series (these are called estimators).
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Telescoping Series
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Consider the following infinite series:
1
1
1
1
n
n
n
We write the terms of the first k terms of the series as follows:
1
1
1
1
1
1
1
1
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ith
1
...
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 Summer '00
 Mark
 Calculus, SmartPen Lectures, Lecture Notes, MATH1004, Kyle Harvey, sK

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