progressions

@ Harsha : i dont exactly know how to create a forum because i joined yesterday only !

@ Ashish: Here's the solution of the progression...

1st term = a₁ = (3¹-1)/3
2nd term = a₂= (3²-1)/3²
3rd term = a₃ = (3³-1)/3³
.
.
.
nth term = a_n = (3ⁿ-1)/3ⁿ = 1 - 3^-n

So
S_n
= Σt_n
= n - Σ(3^-n)
= n - [3^-1 x (3ⁿ-1)/3ⁿ x 3/2]
= n - [1/2 x (3ⁿ-1)/3ⁿ]
= n - (1-3^-n)/2

This is the correct answer buddy.