Thread: Relations between similar limits?

Sorry about the vague title. I've made apost similar to this... Here it goes:

Give an epsilon - N proof that:

if a[n] -> a then a[n]^2 -> a^2

and the same for

if a[n] -> a then a[n]^4 -> a^4

Any Ideas? Again, cheers

Let be given.
By assumption .

Choose N such that for all n>N

Now for the real N, we may need to go bigger depending on the epsilon, we must consider |M| is the maximum value of the sequence past N, at some point the sequence must be bounded if it converges to a. The point is we need to choose N so that for all n>N.



I think you can figure out the second part, remember