Question

有一数列：x1,x2,x3,.,x（n-1）,xn,规定x1=2,x2-x1=4,x3-x2=4,.xn-x（n-1）=

Answer 1

x2-x1=4

x3-x2=6

...

xn-x(n-1)=2n

以上各式相加得到xn-x1=2(2+3+...+n)=2*(2+n)(n-1)/2=(n-1)*(n+2)

即有xn=x1+n^2+n-2=n(n+1)

2/x1+2/x2+...+2/xn=2000/1001

1/1*2+1/2*3+...+1/n(n+1)=1000/1001

1-1/2+1/2-1/3+...+1/n-1/(n+1)=1000/1001

1-1/(n+1)=1000/1001

1/(n+1)=1/1001

n=1000