[tex] \sum_{n=1}^{\infty} \arctan(n+1)-\arctan(n) [/tex].(adsbygoogle = window.adsbygoogle || []).push({});

So we want to take [tex] \lim s_{n} = \lim_{n\rightarrow \infty} (\arctan 2-\arctan 1)+(\arctan 3-\arctan 2) + ... + (\arctan(n+1)-\arctan n) [/tex]. From this I can see all of the terms cancel except [tex] \arctan 1 [/tex]. But then how do we get: [tex] \lim_{n\rightarrow \infty} \arctan(n+1)-\arctan 1 [/tex]? Wouldn't the [tex] \arctan(n+1) [/tex] cancel out?

Thanks

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# Homework Help: Telescoping Series

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