Endless Spin

I spin it again and again,and throw it away finally.
So now I have a row of n ball,named from 1 to n,each ball is white initially.
At each step I randomly chose a interval [l, r] and paint all ball in this interval to black.
It means every interval have a equal chance of being chosen.
And I'll stop if all ball are black.What is the expected steps before I stop?

The first line contains integer T(1<=T<=50). Denoting the number of the test cases.
Then T lines follows, each line contains an integer n (1<=n<=50).

For each test cases,print the answer in a line.
Print the answer rounded to 15 decimal places.

3
1
2
3

1.000000000000000
2.000000000000000
2.900000000000000

不建议使用long double

WJMZBMR

2013 Multi-University Training Contest 3