MHB Prove that the sequence converges to 0 (2)

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e_{n+1} = (e_n-2)/(e_n+4)

Prove that {e_n} converges to 0 if

(a) e_0 > -1

(b) -2 < e_0 < -1

PS: I haven't learned things like sup and inf yet, so please don't use them.
 
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Look at the other question you posted. The idea is very similar.
Also it would help if you post your work so we can help you with your steps.
 
I got it. Thanks!
 

Thread '2-sphere intrinsic definition by gluing disks' boundaries'

A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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