how to solve this partial fraction:
f(x) = 3x/(1+2x)^m
where m is integer 1,2,....,m

Question

how to solve this partial fraction:
f(x) = 3x/(1+2x)^m
where m is integer 1,2,....,m

anonymous · Answer

For m =8
$$
\frac{3 x}{(2 x+1)^8}=\frac{3}{2 (2
   x+1)^7}-\frac{3}{2 (2 x+1)^8}
$$

anonymous · Answer

for m=9
$$
\frac{3 x}{(2 x+1)^9}=\frac{3}{2 (2
   x+1)^8}-\frac{3}{2 (2 x+1)^9}

$$

anonymous · Answer

Can you find a pattern?

anonymous · Answer

Hi
first thank you very much for the answer.
but this is not the case that I need, in my case m is unknown, and then I can't said m=8 or any other number.
the soultion of the bove equation is:
$$\frac{ 3x }{(1+2x)^m } = \sum_{i=1}^{m} \frac{ Ai }{ (1+2x)^i }$$
now I don't know how to find the value of Ai , that is my problem
thank you

anonymous · Answer

All of them are zero except 
$$
A_m=-\frac 3 2 \text {  and } A_{m-1=}\frac 3 2
$$