这两道题怎么简算?计算:(1/2011-1)(1/201-1)(1/2009-1)……(1/3-1)(1/2-1)我们知道:1/2×2/3=1/3,1/2×2/3×3/4=1/4,1/2×2/3×3/4×4/5=1/5,…,1/2×2/3×3/4×…×n/n+1=1/n+1.根据以上规律,解答下面两
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![这两道题怎么简算?计算:(1/2011-1)(1/201-1)(1/2009-1)……(1/3-1)(1/2-1)我们知道:1/2×2/3=1/3,1/2×2/3×3/4=1/4,1/2×2/3×3/4×4/5=1/5,…,1/2×2/3×3/4×…×n/n+1=1/n+1.根据以上规律,解答下面两](/uploads/image/z/1072558-46-8.jpg?t=%E8%BF%99%E4%B8%A4%E9%81%93%E9%A2%98%E6%80%8E%E4%B9%88%E7%AE%80%E7%AE%97%3F%E8%AE%A1%E7%AE%97%EF%BC%9A%EF%BC%881%2F2011-1%EF%BC%89%EF%BC%881%2F201-1%EF%BC%89%EF%BC%881%2F2009-1%EF%BC%89%E2%80%A6%E2%80%A6%EF%BC%881%2F3-1%EF%BC%89%EF%BC%881%2F2-1%EF%BC%89%E6%88%91%E4%BB%AC%E7%9F%A5%E9%81%93%EF%BC%9A1%2F2%C3%972%2F3%EF%BC%9D1%2F3%2C1%2F2%C3%972%2F3%C3%973%2F4%EF%BC%9D1%2F4%2C1%2F2%C3%972%2F3%C3%973%2F4%C3%974%2F5%EF%BC%9D1%2F5%2C%E2%80%A6%2C1%2F2%C3%972%2F3%C3%973%2F4%C3%97%E2%80%A6%C3%97n%2Fn%2B1%EF%BC%9D1%2Fn%2B1.%E6%A0%B9%E6%8D%AE%E4%BB%A5%E4%B8%8A%E8%A7%84%E5%BE%8B%2C%E8%A7%A3%E7%AD%94%E4%B8%8B%E9%9D%A2%E4%B8%A4)
这两道题怎么简算?计算:(1/2011-1)(1/201-1)(1/2009-1)……(1/3-1)(1/2-1)我们知道:1/2×2/3=1/3,1/2×2/3×3/4=1/4,1/2×2/3×3/4×4/5=1/5,…,1/2×2/3×3/4×…×n/n+1=1/n+1.根据以上规律,解答下面两
这两道题怎么简算?
计算:(1/2011-1)(1/201-1)(1/2009-1)……(1/3-1)(1/2-1)
我们知道:1/2×2/3=1/3,1/2×2/3×3/4=1/4,1/2×2/3×3/4×4/5=1/5,…,1/2×2/3×3/4×…×n/n+1=1/n+1.根据以上规律,解答下面两题.
①计算:(1/19-1)(1/20-1)(1/21-1)…(1/97-1)
②将2009减去它的1/2,再减去余下的1/3,再减去余下的1/4/,再减去余下的1/5……依此类推,直到最后减去余下的1/2009,最后结果是多少?
这两道题怎么简算?计算:(1/2011-1)(1/201-1)(1/2009-1)……(1/3-1)(1/2-1)我们知道:1/2×2/3=1/3,1/2×2/3×3/4=1/4,1/2×2/3×3/4×4/5=1/5,…,1/2×2/3×3/4×…×n/n+1=1/n+1.根据以上规律,解答下面两
:(1/2011-1)(1/201-1)(1/2009-1)……(1/3-1)(1/2-1)
=-2010/2011*(-2009/2010)*(-2008/2009)*...*(-2/3)*(-1/2)
=1/2011
2)
(1/19-1)(1/20-1)(1/21-1)…(1/97-1)
=(-18/19)*(-19/20)...(-96/97)
=-18/97
将2009减去它的1/2,再减去余下的1/3,再减去余下的1/4/,再减去余下的1/5……依此类推,直到最后减去余下的1/2009
=2009(1-1/2)(1-1/3)(1-1/4)...(1-1/2009)
=2009*1/2*2/3*3/4*..2008/2009
=2009*1/2009
=1
其实规律不是已经都给定了吗?
原题1=2010/2011*2009/2010*2008/2009*....*2/3*1/2=1/2011
①=-18/19*-19/20*-20/21*....*-96/97=-18/97
②可以转化成2009*1/2*2/3*3/4*....*2008/2009=2009/2009=1