1/1!+1/2!+1/3!+...1/n!

显示全部楼层 · 2009-3-25 20:36:38

N取无穷，整个式子的值是多少？
是阶乘啦～

千问 · 2009-3-25 20:36:38

证明：当k=1时 1/2+1/3+1/4=13/12=26/24>25/24 结论成立。假设k=n时结论成立，即 1/(n+1)+1/(n+2)+1/(n+3)+...+1/(3n+1)>25/24 当k=n+1时由于 9(n+1)^2=9n^2+18n+9>9n^2+18n+8=(3n+2)(3n+4) 即 9(n+1)^2/[(3n+2)(3n+4)]-1>0 左侧为 1/[(n+1)+1]+1/[(n+1)+2]+1/[(n+1)+3]+...+1/[3(n+1)+1] =1/(n+1)+1/(n+2)+1/(n+3)+...+1/(3n+1)+{1/(3n+2)+1/(3n+3)+1/(...

千问 · 2009-3-25 20:36:38

public static void main(String[] args)
{
int n=300;
System.out.println(do1(n));
}
public static double do1(int n)//计算1/n!+....
{
if...