(1x3)/1+(3x5)/1+(5x7)/1+...+(99x101)=?
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(1x3)/1+(3x5)/1+(5x7)/1+...+(99x101)=?
![(1x3)/1+(3x5)/1+(5x7)/1+...+(99x101)=?](/uploads/image/z/17980289-17-9.jpg?t=%281x3%29%2F1%2B%283x5%29%2F1%2B%285x7%29%2F1%2B...%2B%2899x101%29%3D%3F)
1/(1×3)=1/2×(1-1/3)
1/(3×5)=1/2×(1/3-1/5)
裂项法
所以原式=1/2×(1-1/3+1/3-1/5+……+1/99-1/101)=1/2×(1-1/101)=1/2×100/101=50/101
1/(3×5)=1/2×(1/3-1/5)
裂项法
所以原式=1/2×(1-1/3+1/3-1/5+……+1/99-1/101)=1/2×(1-1/101)=1/2×100/101=50/101
1/1x3+1/3x5+1/5x7+……+1/99x101
经典奥数题11/1x3+1/3x5+1/5x7.1/99x101解题思路请写清楚
2/1x3 + 2/3x5 + 2/5x7 +······+ 2/97x99 + 2/99x101 简便计算
1x1-2x2+3x3-4x4+5x5-6x6.-100x100+101x101
1/1X3+1/3X5+1/5X7...1/17X19+1/19X21=
1/1x3+1/3x5+1/5x7+1/7x9+1/9x11=?
1/1x3+1/3x5+1/5x7+.+1/2009x2011=
2/1x3+2/3X5+2/5x7=2/7x9+2/9x11
1/1x3+1/3x5+1/5x7.1/2009x2010+1/2011x2013
计算:1/1x3+1/3x5+1/5x7+...1/2009x2011+1/2011×2013
1/1x3+1/3x5+1/5x7+…+1/2011x2013是多少?
1/(1x3)+1/(3x5)+1/(5x7)+.+1/(2011x2013) 等于什么