`1/9+1/18+1/30+1/45+1/63...`
This is not a geometric series
`1/3(1/3+1/6+1/10+1/15+1/21..)`
`3=1/2(2*3)`
`6=1/2(3*4)`
`10=1/2(9*5)`
`1/2n(n+1)` where `n>=2`
`=1/3*2 sum_(n=2)^(oo)1/(n(n+1))`
`=2/3sum_(n=2)^oo(1/n-1/(n+1))`
`=2/3 lim_(N->oo)sum_(n=2)^N(1/n-1/(n+1))`
`=2/3lim_(N->oo)[1/2-1/(N+1)]`
`=2/3(1/2-0)`
`=1/3`
Option A is correct.
