1又1/3+3又1/15+5又1/35+7又1/63+9又1/99的计算过程,

1又1/3+3又1/15+5又1/35+7又1/63+9又1/99的计算过程,
1又1/3+3又1/15+5又1/35+7又1/63+9又1/99的计算过程,

1又1/3+3又1/15+5又1/35+7又1/63+9又1/99的计算过程,
原式=(1+3+5+7+9)+(1/3+1/15+1/35+1/63+1/99)
=25+0.5x[1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11)]
=25+0.5x[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)]
=25+0.5x(1-1/11)=25又5/11

1+3+5+7+9=25；
1/3=1/2(1-1/3)
1/15=1/2(1/3-1/5)
1/35=1/2(1/5-1/7)
1/63=1/2(1/7-1/9)
1/99=1/2(1/9-1/11)
上面五个式子相加
原式=25+1/2(1-1/11)
=25+5/11=280/11

1又1/3+3又1/15+5又1/35+7又1/63+9又1/99
= (1+1/3)+(3+1/15)+(5+1/35)+(7+1/63)+(9+1/99)
= (1+3+5+7+9)+(1/3+1/15)+(1/35+1/63)+1/99
= 25+(5/15+1/15)+(9/315+5/315)+1/99
= 25+6/15+14/315+1/99
...

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1又1/3+3又1/15+5又1/35+7又1/63+9又1/99
= (1+1/3)+(3+1/15)+(5+1/35)+(7+1/63)+(9+1/99)
= (1+3+5+7+9)+(1/3+1/15)+(1/35+1/63)+1/99
= 25+(5/15+1/15)+(9/315+5/315)+1/99
= 25+6/15+14/315+1/99
= 25+2/5+2/45+1/99
= 25+18/45+2/45+1/99
= 25+20/45+1/99
= 25+4/9+1/99
= 25+44/99+1/99
= 25+45/99
= 25+5/11
= 25又5/11

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