*Originally posted by Acolyte*

**How about:
**

x(n) = 1 if n=1,2 or 3

x(n) = sqrt(2) otherwise

NOTE: There are clearly an infinite number of solutions, so I assume you're just looking for one.

sorry to bother you, but

sqrt(2) - sqrt(2) + sqrt(2) - sqrt(2) + sqrt(2) - sqrt(2) + ...

aint summable (if that is the correct english word for 'sommeerbaar'π

Cause it would be the same as

[sqrt(2) - sqrt(2)] + [sqrt(2) - sqrt(2)] + [sqrt(2) - sqrt(2)] + ...

= 0 + 0 + 0 ... = 0

and as

sqrt(2) + [-sqrt(2) + sqrt(2)] + [-sqrt(2) + sqrt(2)] + ....

= sqrt(2) + 0 + 0 + ... = sqrt(2)

If my thinking is rigth there aint a solution to this question cause therefor the sequence

2/x(1), -x(1), 2/x(2), -x(2), 2/x(3), -x(3), ...

should converge to 0. But that can't be done cause 2/x(n) or x(n) is greater then 1 for all n.