Revision NoteAuthorRogerExpertiseMathsGeometric SeriesHow do I find the sum of a geometric series?A geometric series is the sum of the terms of a geometric sequenceThe following formulae will let you find the sum of the first n terms of a geometric series: or ais the first termris the common ratioThe one on the left is more convenient if r<1, the one on the right is more convenient if r>1The a and the r in those formulae are exactly the same as the ones used with geometric sequencesHow do I prove the geometric series formula?Learn this proof of the geometric series formula – you can be asked to give it in the exam:Write out the sum onceWrite out the sum again but multiply each term byrSubtract the second sum from the firstAll the terms except two should cancel outFactorise and rearrange to makeSthe subjectWhat is the sum to infinity of a geometric series?If (and only if!) |r|<1, then the geometric series converges to a finite value given by the formulaS∞ is known as the sum to infinity...
