2/3*5+2/5*7+2/7*9+2/9*11+...+2/99*101

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2/3*5+2/5*7+2/7*9+2/9*11+...+2/99*101

2/3*5+2/5*7+2/7*9+2/9*11+...+2/99*101
2/3*5+2/5*7+2/7*9+2/9*11+...+2/99*101

2/3*5+2/5*7+2/7*9+2/9*11+...+2/99*101
2/3*5+2/5*7+2/7*9+2/9*11+...+2/99*101
=2/3*3+2/5*5+2/7*7+2/9*9+...+2/99*99+2x2x(1/3+1/5+1/7+1/9+...+1/99)
=2x49+4x[(2-1)/(1+2)+(3-2)/(3+2)``````)
=98+1-1/50
=99-1/50
=98又49/50
有不懂再问,

2/3*5+2/5*7+2/7*9+2/9*11+...+2/99*101
=2×(1/3×5+1/5×7+1/7×9+……+1/99×101)
=2×1/2×(1/3-1/5+1/5-1/7+1/7-1/9+……+1/99-1/101)
=1/3-1/101
=101/303-3/303
=98/303