What is the value of $ \sum_{n=1}^\infty  (\tan^{-1}\sqrt{n}-\tan^{-1}\sqrt{n+1})$?

Your answer should be in radians.
Question:
What is the value of $ \sum_{n=1}^\infty  (\tan^{-1}\sqrt{n}-\tan^{-1}\sqrt{n+1})$?

Your answer should be in radians.
Answer:
Let's think step by step.

user
-\frac{\pi}{4}
What is the value of $ \sum_{n=1}^\infty  (\tan^{-1}\sqrt{n}-\tan^{-1}\sqrt{n+1})$?

Your answer should be in radians.
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