1. From a sequence An, collect even numbered terms En = A2n, and Odd terms O = A2n-1. SHow that An --> L iff En --> L and On --> L(adsbygoogle = window.adsbygoogle || []).push({});

Im not sure if this is true while thinking about the proof but a sequence can behave in any way and therefore the even and odd terms may not necessairly come one after another so we can jus say for some n large enough En will approach the same thing as On. I'm clueless, please give me some idea

2. well if that wasn't enough here's another one( |x| means absolute value)

If An --> L then |An| --> L, is the converse true? That is If |An| -- > |L| then An --> L. Prove or give a counterexample. First of all is this even true? If it isn't then maybe a sequence like (-1/n)-1, maybe? Or does counterexample mean something else?

3. If An --> L and Bn --> L then show that

a1,b1,a2,b2,a3,b3,... converges to L. SO somehow we have to make sure that every term of B is greater than A somehow so obviously Bn> An but An+1 > Bn. I can think of a function that does this but how would you prove it?

Any sort of guidance on ANY of these questions would be greatly appreciated

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# Homework Help: Three problems

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