limit with fractional part

[stuart clark]

\(\displaystyle \lim_{n\to\infty}\left\{\left(\sqrt{3}+1\right)^{2n}\right\} =\)

Where \(\displaystyle \left\{.\right\} =\)fractional part function

 

[tkhunny]

1) It certainly must be bounded on by 0 (lim) and 1 (sup). That's promising.
2) I'm a little puzzled that it uses 'n', rather than 'x'. By convention, 'n' usually means Natural Numbers. I wonder if it would make a difference if we switched to Real Numbers...
3) Testing on your calculator probably fails quickly, as 2.7^n exceeds the maximum possible value of the machine in short order.
4) It may be useful to rewrite the function as mod(number,1). It might graph more easily -- for a little while.

What say you? Your explorations have suggested what?