<s>[INST] Limit of series $4\left( \frac {1}{8}+\frac {1}{12}\right) +6\left( \frac {1}{24}+\frac {1}{36}\right) +\ldots$ How to find this serie 
$4\left( \dfrac {1}{8}+\dfrac {1}{12}\right) +6\left( \dfrac {1}{24}+\dfrac {1}{36}\right) +8\left( \dfrac {1}{64}+\dfrac {1}{96}\right) +\ldots $
I think it's telescopic, isn't it?
 [/INST] multiple the numbers before parantheses then it's formula for the general will be obtained
 $$\sum_{n=1}^\infty(\frac{1}{2\cdot 2^{n-1}}+\frac{1}{3\cdot 2^{n-1}})$$
and it's equal to following geometric serie:
$$\frac{5}{6}\sum_{n=1}^\infty\frac{1}{2^{n-1}}=\frac{10}{6}$$
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