1/1*3+1/3*5+1/3*7+1/7*9+1/9*11怎样简算?为什么?
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1/1*3+1/3*5+1/3*7+1/7*9+1/9*11怎样简算?为什么?
“1/3*7”应该是“1/5*7”吧
1/1*3+1/3*5+1/5*7+1/7*9+1/9*11
=1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+1/2*(1/7-1/9)+1/2*(1/9-1/11)
=1/2*(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=1/2*(1-1/11)
=1/2*10/11
=5/11
1/1*3+1/3*5+1/3*7+1/7*9+1/9*11怎样简算?为什么?第二个加号后是不是1/5*7?
假设Y比较大 1/x*y=(y-x)(1/X-1/Y)
所以上面等式=0.5*(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=5/11
列项求和:
1/1*3=1/2(1-1/3)
1/3*5=1/2(1/3-1/5)
...
1/9*11=1/2(1/9-1/11)
1/1*3+1/3*5+1/3*7+1/7*9+1/9*11=1/2(1-1/11)=5/11
(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
1-3+5-7+...
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+.+1/2n+1
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
1/1*3+1/3*5+1/5*7+1/7*9+.+1/49*51
1/1*3+1/3*5+1/5*7+1/7*9+...+1/2007*2009=?