1/1*3+1/3*5+1/5*7+.+1/49*51怎么计算

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1/1*3+1/3*5+1/5*7+.+1/49*51怎么计算
1/1*3+1/3*5+1/5*7+.+1/49*51怎么计算

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

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

1-3+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