简算1/1*3+1/3*5+1/5*7+...1/99*101

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简算1/1*3+1/3*5+1/5*7+...1/99*101简算1/1*3+1/3*5+1/5*7+...1/99*101简算1/1*3+1/3*5+1/5*7+...1/99*1011/1*3=1

简算1/1*3+1/3*5+1/5*7+...1/99*101
简算1/1*3+1/3*5+1/5*7+...1/99*101

简算1/1*3+1/3*5+1/5*7+...1/99*101
1/1*3=1/2*(1-1/3)
1/1*3+1/3*5+1/5*7+...1/99*101
=1/2*(1-1/3+1/3-1/5+...+1/99-1/101)
=1/2*(1-1/101)
=1/2*100/101
=50/101

1/1*3+1/3*5+1/5*7+...1/99*101
=1/2*(2/1*3+2/3*5+……+2/99*101)
=1/2*(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-……+1/99-1/101)
=1/2*(1-1/101)
=1/2*100/101
=50/101