How do you find the n-th partial sum of a geometric series?

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Answer 1 · 2014-10-22T19:22:09

Let us find a formula for the nth partial sum of a geometric series.

#S_n=a+ar+ar^2+cdots+ar^{n-1}#

by multiplying by #r#,

#Rightarrow rS_n=ar+ar^2+cdots+ar^{n-1}+ar^n#

by subtracting #rS_n# from #S_n#,

#Rightarrow (1-r)S_n=a-ar^n=a(1-r^n)#

(Notice that all intermediate terms are cancelled out.)

by dividing by #(1-r)#,

#Rightarrow S_n={a(1-r^n)}/{1-r}#

I hope that this was helpful.