1. Series problem

The rth term ur, of a series is given by ur=(1/3)2r-2 + (1/3)3r-1
Express ∑nr=1 ur in the form A(1-B/27n) where A and B are constant.
Find the sum of infinity of the series.

2. Re: Series problem

Originally Posted by AuXian
The rth term ur, of a series is given by ur=(1/3)2r-2 + (1/3)3r-1
Express ∑nr=1 ur in the form A(1-B/27n) where A and B are constant.
Find the sum of infinity of the series.

$u_r = v_r + w_r$ where $v_r = \left( \frac{1}{3} \right)^{2r-2}$, $w_r = \left( \frac{1}{3} \right)^{3r-1}$ are in GP with common ratio $\frac{1}{9}$ and $\frac{1}{27}$ respectively. Can you find the sum to $n^{th}$ term of $v_r, w_r$ and simplify?