Previous: The Telescoping and Harmonic Series
Previous: The Telescoping and Harmonic Series
Previous: The Telescoping and Harmonic Series
Recall that our definition of a convergence of an infinite series
was given by the following: if the limit
exists, then the given series is convergent. Otherwise, it is divergent.
We used this definition to study one particular infinite series, the geometric series, whose general form is
A reasonable question to ask would be: can we use the definition of convergence to explore the convergence of other special forms?
Suppose we are asked to determine if the series
or
converge. Clearly, these are not geometric series. How could we determine if they converge? Where would we begin to answer such a question?
Our convergence definition can actually be applied directly to study these two series. In the first series, we can show that it is divergent. In the second series, we can use the definition to show that it converges and find its sum.
This lesson does not include any theory or proofs. For our purposes, it will be sufficient to demonstrate these two special forms with a set of examples.
Previous: The Telescoping and Harmonic Series
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