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1减1/2减1/6减1/12减1/20减省略号简9900/1答案和过程
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1减1/2减1/6减1/12减1/20减省略号简9900/1答案和过程
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答案和解析
1-1/2-1/6-1/12-1/20-.-1/9900
=1-1/(1*2)-1/(2*3)-1/(3*4)-1/(4*5)-.-1/(99*100)
=1-[1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+.+1/(99*100)]
=1-[1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/99-1/100]
=1-[1-1/100]
=1-1+1/100
=1/100
=1-1/(1*2)-1/(2*3)-1/(3*4)-1/(4*5)-.-1/(99*100)
=1-[1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+.+1/(99*100)]
=1-[1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/99-1/100]
=1-[1-1/100]
=1-1+1/100
=1/100
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