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!(Bow)

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- Sep 17th 2012, 07:38 PMAuXianSeries problem
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!(Bow) - Sep 17th 2012, 09:30 PMkalyanramRe: Series problem
$\displaystyle u_r = v_r + w_r$ 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?

- Sep 17th 2012, 10:17 PMAuXianRe: Series problem
Thanks for your solution. It's help me. Thanks!(Wink)