有点麻烦 1*2/1=1-2/1,2*3/1=2/1-3/1,3*4/1=3/1-4/1,你发现了什么规律?请利用这个规律验证1*2/1+2*3/1+3*4/1+...+n(n+1)/1=n+1/n
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![有点麻烦 1*2/1=1-2/1,2*3/1=2/1-3/1,3*4/1=3/1-4/1,你发现了什么规律?请利用这个规律验证1*2/1+2*3/1+3*4/1+...+n(n+1)/1=n+1/n](/uploads/image/z/5325605-53-5.jpg?t=%E6%9C%89%E7%82%B9%E9%BA%BB%E7%83%A6+1%2A2%2F1%3D1-2%2F1%2C2%2A3%2F1%3D2%2F1-3%2F1%2C3%2A4%2F1%3D3%2F1-4%2F1%2C%E4%BD%A0%E5%8F%91%E7%8E%B0%E4%BA%86%E4%BB%80%E4%B9%88%E8%A7%84%E5%BE%8B%3F%E8%AF%B7%E5%88%A9%E7%94%A8%E8%BF%99%E4%B8%AA%E8%A7%84%E5%BE%8B%E9%AA%8C%E8%AF%811%2A2%2F1%2B2%2A3%2F1%2B3%2A4%2F1%2B...%2Bn%28n%2B1%29%2F1%3Dn%2B1%2Fn)
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有点麻烦 1*2/1=1-2/1,2*3/1=2/1-3/1,3*4/1=3/1-4/1,你发现了什么规律?请利用这个规律验证1*2/1+2*3/1+3*4/1+...+n(n+1)/1=n+1/n
有点麻烦
1*2/1=1-2/1,2*3/1=2/1-3/1,3*4/1=3/1-4/1,你发现了什么规律?请利用这个规律验证1*2/1+2*3/1+3*4/1+...+n(n+1)/1=n+1/n
有点麻烦 1*2/1=1-2/1,2*3/1=2/1-3/1,3*4/1=3/1-4/1,你发现了什么规律?请利用这个规律验证1*2/1+2*3/1+3*4/1+...+n(n+1)/1=n+1/n
1/[n*(n+1)]=1/n-1/(n+1)
1/(1*2)+1/(2*3)+...+1/[n(n+1)]
=1-1/2+1/2-1/3+...+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)