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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 $S= (a(r^n-1))/(r-1)$

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

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