式子如下:1 1 1 1 1--- + --- + --- + --- + .+ ---- = 2x3 3x4 4x5 5x6 9900打不上公式,请见如下描述:1/6 + 7/12 + 1/20 + 1/30 + ......+1/9900 =请问结果是多少?怎么个算法?规律应该是分母分别为 2x3 3x4 4x5 5x6 ..
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![式子如下:1 1 1 1 1--- + --- + --- + --- + .+ ---- = 2x3 3x4 4x5 5x6 9900打不上公式,请见如下描述:1/6 + 7/12 + 1/20 + 1/30 + ......+1/9900 =请问结果是多少?怎么个算法?规律应该是分母分别为 2x3 3x4 4x5 5x6 ..](/uploads/image/z/1801022-14-2.jpg?t=%E5%BC%8F%E5%AD%90%E5%A6%82%E4%B8%8B%EF%BC%9A1+1+1+1+1---+%2B+---+%2B+---+%2B+---+%2B+.%2B+----+%3D+2x3+3x4+4x5+5x6+9900%E6%89%93%E4%B8%8D%E4%B8%8A%E5%85%AC%E5%BC%8F%EF%BC%8C%E8%AF%B7%E8%A7%81%E5%A6%82%E4%B8%8B%E6%8F%8F%E8%BF%B0%EF%BC%9A1%2F6+%2B+7%2F12+%2B+1%2F20+%2B+1%2F30+%2B+......%2B1%2F9900+%3D%E8%AF%B7%E9%97%AE%E7%BB%93%E6%9E%9C%E6%98%AF%E5%A4%9A%E5%B0%91%EF%BC%9F%E6%80%8E%E4%B9%88%E4%B8%AA%E7%AE%97%E6%B3%95%EF%BC%9F%E8%A7%84%E5%BE%8B%E5%BA%94%E8%AF%A5%E6%98%AF%E5%88%86%E6%AF%8D%E5%88%86%E5%88%AB%E4%B8%BA+2x3+3x4+4x5+5x6+..)
式子如下:1 1 1 1 1--- + --- + --- + --- + .+ ---- = 2x3 3x4 4x5 5x6 9900打不上公式,请见如下描述:1/6 + 7/12 + 1/20 + 1/30 + ......+1/9900 =请问结果是多少?怎么个算法?规律应该是分母分别为 2x3 3x4 4x5 5x6 ..
式子如下:
1 1 1 1 1
--- + --- + --- + --- + .+ ---- =
2x3 3x4 4x5 5x6 9900
打不上公式,请见如下描述:
1/6 + 7/12 + 1/20 + 1/30 + ......+1/9900 =
请问结果是多少?怎么个算法?规律应该是分母分别为 2x3 3x4 4x5 5x6 .....99x100
式子如下:1 1 1 1 1--- + --- + --- + --- + .+ ---- = 2x3 3x4 4x5 5x6 9900打不上公式,请见如下描述:1/6 + 7/12 + 1/20 + 1/30 + ......+1/9900 =请问结果是多少?怎么个算法?规律应该是分母分别为 2x3 3x4 4x5 5x6 ..
1/(2*3)+1/(3*4)+1/(4*5)+……+1/(98*99)+1/(99*100)
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/98-1/99)+(1/99-1/100)
=1/2-1/100
=49/100=0.49
写清楚点
原式=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+...+(1/99-1/100)
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...+1/99-1/100
=1/2+(1/3-1/3)+(1/4-1/4)+(1/5-1/5)+(1/6-1/6)...+(1/99-1/99)-1/100
=1/2-1/100
=49/100