CK12 Calculus - Single Variable

Usingthenth-Term Test,. Sincethe limit is 0, we cannotmakea conclusionaboutconvergence
or divergence.

Rulesfor ConvergentSeries,Reindexing
Rules
As with sequences,thereare rulesfor convergentinfiniteseriesthat help makeit easierto determinecon-
vergence.

Theorem(Rulesfor ConvergentSeries)1. Suppose and are convergentserieswith

and. Then and are also convergentwhere

and

(The sum or differenceof convergentseriesis also convergent.)2. Let c ≠ 0 be a constant.Suppose

convergesand Then also convergeswhere. If

diverges,then also diverges.(Multiplyingby a nonzeroconstantdoesnot affect convergenceor

divergence.)

Example 10

Find the sum of.
Solution

Usingthe RulesTheorem,.

is a convergentgeometricserieswitha= 2 and. Its sum is.

is a convergentgeometricserieswitha= 2 and. Its sum is.

Then