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調和級數求和

Description

In mathematics, the nth harmonic number is the sum of the reciprocals of the first n natural numbers:

In this problem, you are given n, you have to find Hn.

Input

Input starts with an integer T (≤ 10000), denoting the number of test cases.

Each case starts with a line containing an integer n (1 ≤ n ≤ 108

).

Output

For each case, print the case number and the nth harmonic number. Errors less than 10-8 will be ignored.

Sample Input

12

1

2

3

4

5

6

7

8

9

90000000

99999999

100000000

Sample Output

Case 1: 1

Case 2: 1.5

Case 3: 1.8333333333

Case 4: 2.0833333333

Case 5: 2.2833333333

Case 6: 2.450

Case 7: 2.5928571429

Case 8: 2.7178571429

Case 9: 2.8289682540

Case 10: 18.8925358988

Case 11: 18.9978964039

Case 12: 18.9978964139

最重要的就是找到在大於10000時候的調和級數公式,也是就ln(n+1)+0.5772156649
#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<ctype.h>
#include<math.h>
#include<iostream>
using namespace std; #include<algorithm> #define N 2100 double a[10010]; #define Max 0x3f3f3f3f int main() { int i, n, T, t=1; scanf("%d", &T); while(T--) { a[1]=1; for(i=2;i<10000;i++) { a[i]=a[i-1]+1.0/i; } scanf("%d", &n); printf("Case %d: ", t++); if(n<10000) { /*if(n==1) printf("1\n"); else if(n==2) printf("1.5\n"); else if(n==6) printf("2.450\n"); else*/ printf("%.10f\n", a[n]); } else { double sum; sum=log(n)+0.5772156649+1.0/(2*n); printf("%.10f\n", sum); } } return 0; }