Math Is Fun Forum

mrpace

Member

Registered: 2012-08-16

Posts: 88

Quick question on sequence convergence.

I understand that if a sequence converges to a particular value then we call that sequence convergent.
However, what if the sequence converges to 2 values?

For example the sequence 2/3, -3/5, 4/7, -5/9 approaches -0.5 from below and approaches 0.5 from above. Do we just say that the sequence diverges?

zetafunc

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Registered: 2014-05-21

Posts: 2,436

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Re: Quick question on sequence convergence.

Yes, a sequence does not converge if it converges to two different values (i.e. it diverges). Here, your sequence given by

has two subsequences which converge to two different values depending on whether or not n is odd or even.

You can try constructing a proof by contradiction of what happens when you suppose a sequence converges to two different limits.