x1,x2,x3.xn-1,xn x1=2,x2-x1=4,x3-x2=6...xn-x(n-1）则x6= 当2/x1+2/x2+2/x3...2/xn=2000/1001时

题目

x1,x2,x3.xn-1,xn x1=2,x2-x1=4,x3-x2=6...xn-x(n-1）则x6= 当2/x1+2/x2+2/x3...2/xn=2000/1001时
n的值为

答案

xn-x(n-1)=2n
∴xn=n(n+1)
x6=42
2/1×2 + 2/2×3 + 2/3×4 + …… + 2/n×(n+1)
=2×( 1/1-1/2 + 1/2-1/3 + 1/3-1/4 + …… + 1/n-1/(n+1) )
=2n/(n+1)
n=1000