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*1012/3*5+2/5*7+2/7*9+2/9*11+…2/99*1012/3*5+2/5*7+2/7*9+2/9*11+…2/99*1

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
=(1/3-1/5)+(1/5-1/7)+……+(1/99-1/101)
=1/3-1/101
=98/303

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

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+1/9*11+...+1/99*101)
=2*(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+...+1/99-1/101)
=2*(1/3-1/101)
=2*98/303
=196/303