Compute $$\sum_{n=1}^{\infty} \left( \frac{2n}{3^n} - \frac{1}{2^n} \right).$$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Compute $$\sum_{n=1}^{\infty} \left( \frac{2n}{3^n} - \frac{1}{2^n} \right).$$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1}{2}
Compute $$\sum_{n=1}^{\infty} \left( \frac{2n}{3^n} - \frac{1}{2^n} \right).$$
train