初一数学奥数题求1/3*7+1/7*11+1/11*15+……+1/55*59 1/3*7+1/7*11+1/11*15+…+1/55*59
1/3*7+1/7*11+1/11*15+...+1/55*59=?\u56e0\u4e3a1/3*7=1/21=1/4*\uff081/3-1/7\uff09
\u6240\u4ee5,\u539f\u5f0f=1/4*\uff081/3-1/7\uff09+1/4*(1/7-1/11)+\u2026\u20261/4*(1/55-1/59)
=1/4(1/3-1/7+1/7-1/11+\u2026\u20261/55-1/59)
=1/4*(1/3-1/59)
=14/177
=1/4(1/3-1/7+1/7-1/11....+1/55-1/59)
=1/4*(1/3-1/59)
14/177
1/7*11=1/4(1/7-1/11)
...
原式=1/4[(1/3-1/7)+(1/7-1/11)+(1/11-1/15)+...+(1/55-1/59)]
=1/4(1/3-1/59)
=1/4*(59-3)/177
=14/177
1/3*7+1/7*11+1/11*15+……+1/55*59=1/4*（1/3-1/7+1/7-1/11+……+1/55-1/59）=1/4*（1/3-1/59）
下面的自己慢慢算
1/3*7+1/7*11+1/11*15+……+1/55*59
=1/4*(1/3-1/7+1/7-1/11+1/11-1/15+...+1/55-1/59)
=1/4*(1/3-1/59)
=1/4*(59/177-3/177)
=1/4*56/177
=14/177
14/177
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绛旓細鍘熷紡=1/4[(1/3-1/7)+(1/7-1/11)+(1/11-1/15)+...+(1/55-1/59)]=1/4(1/3-1/59)=1/4*(59-3)/177 =14/177
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