先观察,在计算:已知:1-1/2=1/1-1/2=1/(1×2),1/2-1/3=1/(2*3),1/3-1/4=1/(3×4)……求“1/(1*3)+1/(3*5)+1/(5*7)+……=1/(99*101)
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![先观察,在计算:已知:1-1/2=1/1-1/2=1/(1×2),1/2-1/3=1/(2*3),1/3-1/4=1/(3×4)……求“1/(1*3)+1/(3*5)+1/(5*7)+……=1/(99*101)](/uploads/image/z/7185149-53-9.jpg?t=%E5%85%88%E8%A7%82%E5%AF%9F%2C%E5%9C%A8%E8%AE%A1%E7%AE%97%EF%BC%9A%E5%B7%B2%E7%9F%A5%EF%BC%9A1%EF%BC%8D1%2F2%3D1%2F1-1%2F2%3D1%2F%EF%BC%881%C3%972%EF%BC%89%2C1%2F2-1%2F3%3D1%2F%EF%BC%882%2A3%EF%BC%89%2C1%2F3-1%2F4%3D1%2F%EF%BC%883%C3%974%EF%BC%89%E2%80%A6%E2%80%A6%E6%B1%82%E2%80%9C1%2F%EF%BC%881%2A3%EF%BC%89%2B1%2F%EF%BC%883%2A5%EF%BC%89%2B1%2F%EF%BC%885%2A7%EF%BC%89%2B%E2%80%A6%E2%80%A6%3D1%2F%EF%BC%8899%2A101%EF%BC%89)
先观察,在计算:已知:1-1/2=1/1-1/2=1/(1×2),1/2-1/3=1/(2*3),1/3-1/4=1/(3×4)……求“1/(1*3)+1/(3*5)+1/(5*7)+……=1/(99*101)
先观察,在计算:
已知:1-1/2=1/1-1/2=1/(1×2),1/2-1/3=1/(2*3),1/3-1/4=1/(3×4)……
求“1/(1*3)+1/(3*5)+1/(5*7)+……=1/(99*101)
先观察,在计算:已知:1-1/2=1/1-1/2=1/(1×2),1/2-1/3=1/(2*3),1/3-1/4=1/(3×4)……求“1/(1*3)+1/(3*5)+1/(5*7)+……=1/(99*101)
1/(1*3)+1/(3*5)+1/(5*7)+……+1/(99*101)
= 1/2 * (1-1/3) + 1/2 * (1/3-1/5) + 1/2 * (1/5-1/7) + .+ 1/2 * (1/99-1/101)
= 1/2 * (1 - 1/101)
= 50/101
请问你这道题求的有木有问题啊???是不是应该求1/(1*3)+1/(3*5)+1/(5*7)+……+1/(99*101)=???
是不是这样???如果是这样我就试求一下:
根据已知能知道(1-1/2)+(1/2-1/3)=1/(1×2)+1/(2*3)=1*1/2+1/2*1/3
提取1/2并整理,则1-1/3=1/2+1/6 ...
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请问你这道题求的有木有问题啊???是不是应该求1/(1*3)+1/(3*5)+1/(5*7)+……+1/(99*101)=???
是不是这样???如果是这样我就试求一下:
根据已知能知道(1-1/2)+(1/2-1/3)=1/(1×2)+1/(2*3)=1*1/2+1/2*1/3
提取1/2并整理,则1-1/3=1/2+1/6
求出,1/3=1-(1/2+1/6)
1/3=1/2-1/6
1/3=1/2(1-1/3)即,1/(1*3)=1/2(1-1/3)
同理可证:1/(3*5)=1/2(1/3-1/5)
求的是:1/(1*3)+1/(3*5)+1/(5*7)+……+1/(99*101)
=1/2(1-1/3)+1/2(1/3-1/5)+……+1/2(1/99-1/101)
=1/2(1-1/3+1/3-1/5+ ……+1/99-1/101)
=1/2(1-1/101)
=1/2*100/101
=50/101
希望你喜欢这个答案,如果我猜的有错误你再追问我啊!!!!嘿嘿…………
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