# finding value of summation of infinite series

• May 4th 2010, 05:18 AM
WartonMorton
finding value of summation of infinite series
summation from k=0 to infinity of (3^(k-1))/(4^(3k+1)).

Using the seq( and sum( functions on my calculator I get 16/183, but how do I do this without using a calculator.

I wrote out the first few terms but nothing seemed to cross out.

Thanks.
• May 4th 2010, 05:23 AM
mr fantastic
Quote:

Originally Posted by WartonMorton
summation from k=0 to infinity of (3^(k-1))/(4^(3k+1)).

Using the seq( and sum( functions on my calculator I get 16/183, but how do I do this without using a calculator.

I wrote out the first few terms but nothing seemed to cross out.

Thanks.

Note that the thing you're summing can be written as $\frac{1}{12} \left(\frac{3}{4^3} \right)^k$.