Find the sum of the first 20 terms of the series. 1+3+9+27+...

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tiburtius eNotes educator| Certified Educator

This is geometric series with first term `a_1=1` and ratio `r=3`.

Sum of the first `n` terms of geometric series is

`S_n=a_1 (r^n-1)/(r-1)`

Hence sum of the first 20 terms is ` `

`S_20=(3^20-1)/(3-1)=(3^20-1)/2=1743392200`