Compute
\[\sum_{n = 1}^{9999} \frac{1}{(\sqrt{n} + \sqrt{n + 1})(\sqrt[4]{n} + \sqrt[4]{n + 1})}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Compute
\[\sum_{n = 1}^{9999} \frac{1}{(\sqrt{n} + \sqrt{n + 1})(\sqrt[4]{n} + \sqrt[4]{n + 1})}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
9
Compute
\[\sum_{n = 1}^{9999} \frac{1}{(\sqrt{n} + \sqrt{n + 1})(\sqrt[4]{n} + \sqrt[4]{n + 1})}.\]
train