观察下列各等式:1/1×2=1/1-1/2,1/2×3=1/2-1/3,1/3×4=1/3-1/4,……,根据你发现的规律计算:2/1×2+2/2×3+2/3×4++……+2/n(n+1)=————(n为正整数)
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![观察下列各等式:1/1×2=1/1-1/2,1/2×3=1/2-1/3,1/3×4=1/3-1/4,……,根据你发现的规律计算:2/1×2+2/2×3+2/3×4++……+2/n(n+1)=————(n为正整数)](/uploads/image/z/7106686-70-6.jpg?t=%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E5%90%84%E7%AD%89%E5%BC%8F%EF%BC%9A1%2F1%C3%972%3D1%2F1-1%2F2%2C1%2F2%C3%973%3D1%2F2-1%2F3%2C1%2F3%C3%974%3D1%2F3-1%2F4%2C%E2%80%A6%E2%80%A6%2C%E6%A0%B9%E6%8D%AE%E4%BD%A0%E5%8F%91%E7%8E%B0%E7%9A%84%E8%A7%84%E5%BE%8B%E8%AE%A1%E7%AE%97%EF%BC%9A2%2F1%C3%972%2B2%2F2%C3%973%2B2%2F3%C3%974%2B%2B%E2%80%A6%E2%80%A6%2B2%2Fn%EF%BC%88n%2B1%EF%BC%89%3D%E2%80%94%E2%80%94%E2%80%94%E2%80%94%EF%BC%88n%E4%B8%BA%E6%AD%A3%E6%95%B4%E6%95%B0%EF%BC%89)
观察下列各等式:1/1×2=1/1-1/2,1/2×3=1/2-1/3,1/3×4=1/3-1/4,……,根据你发现的规律计算:2/1×2+2/2×3+2/3×4++……+2/n(n+1)=————(n为正整数)
观察下列各等式:1/1×2=1/1-1/2,1/2×3=1/2-1/3,1/3×4=1/3-1/4,……,根据你发现的规律计算:2/1×2+2/2×3+2/3×4++……+2/n(n+1)=————(n为正整数)
观察下列各等式:1/1×2=1/1-1/2,1/2×3=1/2-1/3,1/3×4=1/3-1/4,……,根据你发现的规律计算:2/1×2+2/2×3+2/3×4++……+2/n(n+1)=————(n为正整数)
1-1/(n+1)
(1)1/n-1/n+1
(2)1-1/2007=2006/2007
1-1/n+1
(3)因为1/2*4=(1/2-1/4)/2……
1/2006*2008=(1/2006-1/2008)/2
所以,
原式=(1/2-1/4+1/4-1/6+1/6-1/8+…+1/2006-1/2008)/2
=(1/2-1/2008)/2=1003/4016
n/n+1
你好:
原式=2x(1-1/n+1)
=2xn/n+1
2n/n+1
如果满意记得采纳!
求好评!
(*^__^*) 嘻嘻……
2n/(n+1)