thoughfor reindexing.
Example 13
is a convergentgeometricseries.It can be reindexedby changingthe startingpositionofiand
the powerofi. The new seriesis still convergent.
You can checkthat the serieson the right is the sameseriesas the one of the left by writingout the first
few termsfor eachseries.Noticethat the termsare still in order.
ReviewQuestions
- Expressthe number as an infiniteseries.
- Find and for.
- Determineif the infiniteseries convergesor diverges.
- Whatare the valuesofaandrfor the geometricseries
Determineif eachinfiniteseriesconvergesor diverges.If a seriesconverges,find its sum.
5.
6.
7.
8.
- Find the sum of.