1/1*3+1/3*5+1/5*7+.+1/49*51怎么算啊?

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1/1*3+1/3*5+1/5*7+.+1/49*51怎么算啊?

1/1*3+1/3*5+1/5*7+.+1/49*51怎么算啊?
1/1*3+1/3*5+1/5*7+.+1/49*51怎么算啊?

1/1*3+1/3*5+1/5*7+.+1/49*51怎么算啊?
1/1×3+1/3×5＋1/5×7+…＋1/49×51
=1/2×[1-1/3]+1/2×[1/3-1/5]+1/2×[1/5-1/7]+...+1/2×[1/49-1/51]
=1/2×[1-1/3+1/3-1/5+1/5-1/7+.+1/49-1/51]
=1/2×[1-1/51]
=1/2×50/51
=25/51

1/1*3就是 (1-1/3)/2
1/3*5就是 (1/3-1/5)/2
你逐项拆开就能发现很多个分数都能消去。
最后剩下(1-1/51)/2


1/1*3=(1/2)×(1/1-1/3)
1/3*5=(1/2)×(1/3-1/5)
1/5*7=(1/2)×(1/5-1/7)
...
1/49*51=(1/2)×(1/49-1/51)
1/1*3+1/3*5+1/5*7+......+1/49*51
=(1/2)×(1/1-1/3+1/3-1/5+1/5-1/7+....+1/49-1/51)
=(1/2)×(1/1-1/51)
=(1/2)×50/51
=25/51

原式等于1/2(1-1/3+1/3-1/5......+1/49-1/51)
=1/2(1-1/51)
=25/51

1/2[2/(1*3)+2/(3*5)+2/(5*7)…2/(49*51)]
=1/2(1-1/3+1/3-1/5+1/5-1/7+…1/49-1/50)
=1/2*50/51
=50/102=25/51

好了

解析：
1/[n(n+2)]=(1/2)[(n+2)-n]/[n(n+2)]=(1/2)[1/n-1/(n+2)]
∴原式
=(1/2)*[1-1/3+1/3-1/5+1/5-1/7+…………+1/49-1/51]
=(1/2)*[1-1/51]
=(1/2)*50/51
=25/51
不懂欢迎再问
谢谢

1-3+5-7+... (1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)*(1/3+1/5+1/7) 简算(1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)*(1/3+1/5+1/7) 简便计算 1/1*3+1/1*3*5+1/1*3*5*7+1/1*3*5*7*9-73/945 (1/3+1/5+1/7)*(1/5+1/7+1/9)-(1/3+1/5+1/7+1/9)*(1/5+1/7)=? 1/3+1/5+1/7+.+1/2n+1 1/1*3*5+1/3*5*7+1/5*7*9.+1/95*97*99 1/1×3+1/3×5+1/5×7+1/7×9.+1/2011×2013 简算:1/1*3+1/3*5+1/5*7+1/7*9+1/9*11 1/1*3+1/3*5+1/5*7+1/7*9+...1/17*19= 计算1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+.+1/(19×21) 1/1×3+1/3×5+1/5×7+1/7×9+.+1/2013×2015 1/1*3+1/3*5+1/5*7+1/7*9+.+1/101*103 帮帮忙1/1*3+1/3*5+1/5*7+1/7*9+...1/99*101 1/1*3+1/3*5+1/5*7+1/7*9+1/49*51= 计算：1/1×3+1/3×5+1/5×7+1/7×9``````+1/2001×2003 (1*3)/1+(3*5)/1+(5*7)/1+(7*9)/1+(9*11)/1 1/1*3+1/3*5+1/5*7+1/7*9+1/9*11 (1*3)/1+(3*5)/1+(5*7)/1+(7*9)/1+(9*11)/1