Question

The sequence {xn} tends to zero.

a) Could there be members bigger than 1000000 in this sequence?
b) Could all the members of this sequence be negative?
c) Could all the members of this sequence be bigger than 0.000001?

Answer 1

a) Yes. E.g. the sequence xn = 1/n (when n < 10^(-6));
b) Yes. E.g. the sequence xn = −1/n (n > 0);
c) No. In this case the sequence would be limited at least by 0.000001 (not by zero).