1/1*3+1/3*5+1/5*7+...+1/95*97+1/97*99

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1/1*3+1/3*5+1/5*7+...+1/95*97+1/97*991/1*3+1/3*5+1/5*7+...+1/95*97+1/97*991/1*3+1/3*5+1/5*7+...+1/95

1/1*3+1/3*5+1/5*7+...+1/95*97+1/97*99
1/1*3+1/3*5+1/5*7+...+1/95*97+1/97*99

1/1*3+1/3*5+1/5*7+...+1/95*97+1/97*99
∵1/1*3=1/2*(1/1-1/3)
1/3*5=1/2*(1/3-1/5)
1/5*7=1/2*(1/5-1/7)
……
1/95*97=1/2*(1/95-1/97)
1/97*99=1/2*(1/97-1/99)
∴原式就=1/2*(1/1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+……+1/2*(1/95-1/97)+1/2*(1/97-1/99)
=1/2*(1/1-1/3+1/3-1/5+1/5-1/7+……+1/95-1/97+1/97-1/99)
=1/2*(1-1/99)
=1/2*(98/99)
=49/99

=0.5*(1/1-1/3)+0.5*(1/3-1/5)........=0.5*(1-1/99)
=49/99

1/1*3=0.5*(1/1-1/3)
化简得到
=0.5*(1-1/3+1/3-1/5...+1/97-1/99)
=49/99