1/1*2+1/2*3+1/3*4+.+1/99*100怎样简便运算
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![1/1*2+1/2*3+1/3*4+.+1/99*100怎样简便运算](/uploads/image/z/66395-11-5.jpg?t=1%2F1%2A2%2B1%2F2%2A3%2B1%2F3%2A4%2B.%2B1%2F99%2A100%E6%80%8E%E6%A0%B7%E7%AE%80%E4%BE%BF%E8%BF%90%E7%AE%97)
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1/1*2+1/2*3+1/3*4+.+1/99*100怎样简便运算
1/1*2+1/2*3+1/3*4+.+1/99*100怎样简便运算
1/1*2+1/2*3+1/3*4+.+1/99*100怎样简便运算
1/1*2+1/2*3+1/3*4+.+1/99*100
=1-1/2+1/2-1/3+1/3-1/4+.+1/99-1/100
=1-1/100
=99/100
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/98-1/99)+(1/99-1/100)
=1-1/100
=99/100