- #1
Tommy941
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Homework Statement
Let an → 2. Prove from first principles (i.e. give a direct ε-N proof) that an2 → 4.
Homework Equations
The Attempt at a Solution
I have tried considering |an-2|2 and considering that |an2-4| = |(an+2)(an-2)| but I could not get either of these methods to work. Would someone be able to point me in the right direction?
I was thinking maybe one of the sequences is a subsequence of the other?
I was also wondering, is this true generally that if a sequence tends to L then the sequence squared will tend to L2?
Thanks,
Tommy