Previous: Videos on Telescoping and Harmonic Series
Next: Unit 2: Convergence Tests
Previous: Videos on Telescoping and Harmonic Series
Next: Unit 2: Convergence Tests
Previous: Videos on Telescoping and Harmonic Series
Next: Unit 2: Convergence Tests
We were able to show that
is divergent. It can be shown that
is also divergent, where is any real number. Observe that
The first sum is a constant, while the second sum is the harmonic series, which is divergent.
One might ask how to identify an infinite telescoping series. It may seem a bit obvious, but for the sake of completeness, a telescoping series could have the form
where integers and satisfy . Indeed, one could imagine more complicated forms of telescoping series, but for our purposes, this will be sufficient. Students will only need to be familiar with this form of the telescoping series.
Computing sums of telescoping series can involve having able to compute a partial fraction decomposition. If you would like additional practice with telescopic series that use partial fractions, you can find additional examples that involve the telescoping series in the Additional Resources section within this lesson.
Previous: Videos on Telescoping and Harmonic Series
Next: Unit 2: Convergence Tests
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