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Steinberg – Hypersonic 2.0 (Rebuild SynsoEmu) – AiR

Steinberg – Hypersonic 2.0 (Rebuild SynsoEmu) – AiR



 
 
 
 
 
 
 

Steinberg – Hypersonic 2.0 (Rebuild SynsoEmu) – AiR

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Steinberg – Hypersonic 2.0 (Rebuild SynsoEmu) – AiR.rar zippyshare. com.Q:

Formula for this series?

I have a series I am trying to simplify to the following formula
$a_n=\frac{1}{n+2}$
$b_n=\frac{1}{n+4}$
$c_n=\frac{1}{n+6}$
The answer I want is
$\sum_{n=1}^\infty a_nb_nc_n=?$
The problem is I don’t know how to get to it, I tried a bunch of stuff but i’m stuck.

A:

Hint:
$$
\begin{align*}
a_n+b_n&=\frac 1{n+2}+\frac 1{n+4}\\
&=\frac{n+2+n+4}{n+2n+4}\\
&=\frac{n^2+2n+6} {n^2+4n+8}\\
&=\frac{n^2+2n+6}{(n+2)^2}\\
&=\frac{n^2+n(2+2)+6}{(n+2)^2}\\
&=\frac{(n+2)^2+2n+6}{(n+2)^2}\\
&=\frac 1{n+2}\cdot\frac 1{(n+2)^2}+\frac 1{n+4}\cdot\frac 1{(n+4)^2}\\
&=\frac 1{(n

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