Hello, this is a question we had on an exam and I can't figure it out. Our professors won't publish solutions so I'd be glad for your help.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Prove the following series converges and calculate its limit.

[tex] 0 < a_0 < \frac {\pi}{2} [/tex]

[tex]sin(a_n)= \frac {a_n}{a_{n+1}} [/tex]

and so [tex] 1 > sin(a_0)= \frac {a_0}{a_{1}} [/tex] therefore [tex]a_{1}> a_0 [/tex]

At first I thought this was simple and the sequence converges to [tex] \frac {\pi}{2} [/tex]

But I realised that the inequality can hold for any n, i.e [tex] a_{n+1}> a_n [/tex] because we have no way of knowing by how much it is bigger. This one was on our exam and no one I talked to managed to overcome this little detail.

Some pointers would be greatly apreciated.

Thanks

Tal

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# Homework Help: Convergence of a sequence

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