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#1+3+3^2+............................+3^(n-1)=(3^(n)-1)/2#

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Answer 1 · 2018-04-23T17:46:48

This is a Geometric series.

Here common ratio #r= 3#

Total number of terms #=n#

First term #a=1#

The Sum of Geometric series is given by #S= (a(r^n-1))/(r-1)#

#S=(1(3^n-1))/(3-1)#

#:.S=(3^n-1)/2#