1/2=1/1×2=1/1-1/2 1/6=1/2×3=1/2-1/3 1/12=1/3×4=1/3-1/4 ··· 1.求规律

Question

2.利用规律计算 1/2+1/6+1/12······+1/（n-1)n +1/(n+1)n
3.利用规律解方程 1/（x-4)(x-3) +1/(x-3)(x-2) +1/(x-2)(x-1) +1/(x-1)x +1/(x+1)x =1/x+1

详细点 会的快点啊

Answer 1

1/2=1/1×2=1/1-1/2 1/6=1/2×3=1/2-1/3 1/12=1/3×4=1/3-1/4 ···
1.求规律1/n(n+1)=1/n-1/(n+1）
2.利用规律计算
1/2+1/6+1/12······+1/（n-1)n +1/(n+1)n
=1-1/2+1/2-1/3+1/3-1/4+……+1/（n-1)-1/n+1/n-1/(n+1）
=1-1/（n+1)
=n/(n+1)
3.利用规律解方程
1/（x-4)(x-3) +1/(x-3)(x-2) +1/(x-2)(x-1) +1/(x-1)x +1/(x+1)x =1/(x+1)
1/(x-4)-1/(x-3)+1/(x-3)-1/(x-2）+1/（x-2)-1/(x-1）+1/（x-1)-1/x+1/x-1/(x+1)=1/(x+1)
1/(x-4)-1/(x+1)=1/(x+1）
1/（x-4)=2/(x+1）
2（x-4)=x+1
2x-8=x+1
x=9本回答被提问者采纳

Answer 2

1/2=1/1×2=1/1-1/2 1/6=1/2×3=1/2-1/3 1/12=1/3×4=1/3-1/4 ···
1.求规律1/n(n+1)=1/n-1/(n+1）
2.利用规律计算
1/2+1/6+1/12······+1/（n-1)n +1/(n+1)n
=1-1/2+1/2-1/3+1/3-1/4+……+1/（n-1)-1/n+1/n-1/(n+1）
=1-1/（n+1)
=n/(n+1)
3.利用规律解方程
1/（x-4)(x-3) +1/(x-3)(x-2) +1/(x-2)(x-1) +1/(x-1)x +1/(x+1)x =1/(x+1)
1/(x-4)-1/(x-3)+1/(x-3)-1/(x-2）+1/（x-2)-1/(x-1）+1/（x-1)-1/x+1/x-1/(x+1)=1/(x+1)
1/(x-4)-1/(x+1)=1/(x+1）
1/（x-4)=2/(x+1）
2（x-4)=x+1
2x-8=x+1
x=9