(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For the sequence defined recursively as follows:

a_1 = 2, and a_(n+1) = 1/ (a_n)^2 for all n from N.

2. Relevant equations

So, we are supposed to use induction to first fidn if the sequence increases or decreases, and then use induction again to show if it is bounded.

3. The attempt at a solution

If one would take some terms for this sequence, it is easy to see it is oscillating...

a_1 = 2, a_2 = 1/4, a_3 = 16, a_4 = 1/256.....so I am stuck trying to prove this is an oscillating sequence using induction. is there any other type of proof to use for this case, because induction seems useless in this case.

If someone has any idea, let me know please.

Thank you in advance for you help!

Emira

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# Homework Help: Advanced calculus proof- oscillating sequences

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