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.