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# Find an N such that the convergent sequence is within ε of its limit

Consider the convergent sequence with terms defined by

Let . Find the value of and values of such that for all for each of the following values of :

1. ,
2. ,
3. ,
4. ,
5. .

First, we know

So then we have,

Thus, if then for every we have . We compute for the given values of as follows:

1. implies .
2. implies .
3. implies .
4. implies .
5. implies .

1. Roberto Furini Filho says:

N>1 , N>10, N>100…..N>10000

• Anonymous says:

Greetings!

I think you mean n>1, n>10, as \textbf{N refers to the natural number n has to be larger than} for to be true.

Cheers!

• Anonymous says:

Roberto Furini Filho is right since $n\geN$.