(1+2/3+2+3/4+3+4/5+……+97+98/99+98+99/100)/(3+1/3+5+2/4+7+3/5

问题描述:

(1+2/3+2+3/4+3+4/5+……+97+98/99+98+99/100)/(3+1/3+5+2/4+7+3/5+……+195+97/99+197+98/100)=()
1个回答 分类:数学 2014-10-16

问题解答:

我来补答
(1+2/3+2+3/4+3+4/5+……+97+98/99+98+99/100)/(3+1/3+5+2/4+7+3/5+……+195+97/99+197+98/100)
=[(1+2+3+……+98)+(2/3+3/4+4/5+……+99/100)]/[(3+5+……+197)+(1/3+2/4+……+98/100)]
=[99×49+98-(1/3+1/4+……+1/100)]/[100×98+98-2×(1/3+1/4+……+1/100)]
=[101×49-(1/3+1/4+……+1/100)]/[101×98-2×(1/3+1/4+……+1/100)]
=1/2
 
 
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