# For a Geometric Series explain how you can tell if the series converges or diverges as you keep adding an infinite number of terms to the series. Be sure that your explanation is clear on what it means to converge or diverge. Show using an example(s).

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jimmyrepinIt will converge if the common factorÂ rÂ is between 0 and 1. For example:- Â A GS withÂ first term a1 = 2Â and d = 1/2,Â Â theÂ terms are:- 2 , 1 , 1/2, 1/4, 1/8,1/16 and so on Each term gets smaller and smaller and they will become very small - close to 0.Â Â The sum will converge to a certain value also. In this case it will converge toÂ 2Â /( 1 - 1/2) = 4 If d > 1Â the terms will increase without bounds and the sum gets bigger and bigger . The seriesÂ diverges. for exampleÂ 2, 8, 32, 128, 512 ....Â where a1 = 2 and d = 4.