Using progression, find the sum of first five terms of the series `1+2/3+4/9+…..`

Explanation

Here `a=1` and `r=2/3`
.
`S_n=a(1-r^n)/1-r=[1-(2/3)^n]/1-2/3=3[1-(2/3)^n]`

In particular, `S_5=3[1-(2/3)^5]=3 xx 211/243=211/81`