一乘三分之一加三乘五分之一加五乘七分之一加······加九十七乘一百零一分之一,等于多少.因为1/(1*3)=1/2*(1/1-1/3)分解2=3-1=5-3=7-5=-=101-99所以 1/1*3+1/3*5+1/5*7+-+1/99*101 =1/2(2/1*3+2/3*5++
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![一乘三分之一加三乘五分之一加五乘七分之一加······加九十七乘一百零一分之一,等于多少.因为1/(1*3)=1/2*(1/1-1/3)分解2=3-1=5-3=7-5=-=101-99所以 1/1*3+1/3*5+1/5*7+-+1/99*101 =1/2(2/1*3+2/3*5++](/uploads/image/z/98197-61-7.jpg?t=%E4%B8%80%E4%B9%98%E4%B8%89%E5%88%86%E4%B9%8B%E4%B8%80%E5%8A%A0%E4%B8%89%E4%B9%98%E4%BA%94%E5%88%86%E4%B9%8B%E4%B8%80%E5%8A%A0%E4%BA%94%E4%B9%98%E4%B8%83%E5%88%86%E4%B9%8B%E4%B8%80%E5%8A%A0%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%E5%8A%A0%E4%B9%9D%E5%8D%81%E4%B8%83%E4%B9%98%E4%B8%80%E7%99%BE%E9%9B%B6%E4%B8%80%E5%88%86%E4%B9%8B%E4%B8%80%2C%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91.%E5%9B%A0%E4%B8%BA1%2F%EF%BC%881%2A3%EF%BC%89%3D1%2F2%2A%281%2F1-1%2F3%29%E5%88%86%E8%A7%A32%3D3-1%3D5-3%3D7-5%3D-%3D101-99%E6%89%80%E4%BB%A5+1%2F1%EF%BC%8A3%2B1%2F3%EF%BC%8A5%2B1%2F5%EF%BC%8A7%2B-%2B1%2F99%EF%BC%8A101+%3D1%2F2%282%2F1%EF%BC%8A3%2B2%2F3%EF%BC%8A5%2B%2B)
一乘三分之一加三乘五分之一加五乘七分之一加······加九十七乘一百零一分之一,等于多少.因为1/(1*3)=1/2*(1/1-1/3)分解2=3-1=5-3=7-5=-=101-99所以 1/1*3+1/3*5+1/5*7+-+1/99*101 =1/2(2/1*3+2/3*5++
一乘三分之一加三乘五分之一加五乘七分之一加······加九十七乘一百零一分之一,等于多少.
因为1/(1*3)=1/2*(1/1-1/3)分解2=3-1=5-3=7-5=-=101-99所以 1/1*3+1/3*5+1/5*7+-+1/99*101 =1/2(2/1*3+2/3*5++-+2/99*101) =1/2(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101) =1/2(1-1/101) =50/101
一乘三分之一加三乘五分之一加五乘七分之一加······加九十七乘一百零一分之一,等于多少.因为1/(1*3)=1/2*(1/1-1/3)分解2=3-1=5-3=7-5=-=101-99所以 1/1*3+1/3*5+1/5*7+-+1/99*101 =1/2(2/1*3+2/3*5++
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 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + …… + 1/99 - 1/101)
= (1/2)×( 1 - 1/101)
= (1/2)×(100/101)
= 50/101