Math Is Fun Forum

sumpm1

Member

Registered: 2007-03-05

Posts: 42

Real Analysis Help

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Real Analysis Help

To prove that a convergent sequence is bounded, use the definition of convergence to say:

(where L is the limit of the sequence)

Then no element past x_N will be greater than L+1.
The number of elements before x_N is finite, so you can find max{x_1, x_2, ..., x_N, L+1}.
This is an upper bound for the sequence.

The second theorem you put is what I would use to define divergence to ∞, so without knowing your definition of divergence I can't help you there.

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Why did the vector cross the road?
It wanted to be normal.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Real Analysis Help

sumpm1 is not asking you to prove the theorems. He/She is asking you to use the theorems to prove the two questions.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Real Analysis Help

The theorem you should be using for #2 should be:

Last edited by JaneFairfax (2009-04-10 08:18:24)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Real Analysis Help

Last edited by JaneFairfax (2009-04-10 09:35:55)