The r^{th} term u_{r}, of a series is given by u_{r}=(1/3)^{2r-2} + (1/3)^{3r-1}
Express ∑^{n}_{r=1 }u_{r }in the form A(1-B/27^{n}) where A and B are constant.
Find the sum of infinity of the series.
Please help me! Thank you!
$\displaystyle u_r = v_r + w_r$ where $\displaystyle v_r = \left( \frac{1}{3} \right)^{2r-2}$, $\displaystyle w_r = \left( \frac{1}{3} \right)^{3r-1}$ are in GP with common ratio $\displaystyle \frac{1}{9}$ and $\displaystyle \frac{1}{27}$ respectively. Can you find the sum to $\displaystyle n^{th}$ term of $\displaystyle v_r, w_r$ and simplify?