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 :

- ,
- ,
- ,
- ,
- .

First, we know

So then we have,

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

- implies .
- implies .
- implies .
- implies .
- implies .

N>1 , N>10, N>100…..N>10000

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!

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