数列题一道,具体见图如图所示
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![数列题一道,具体见图如图所示](/uploads/image/z/4351136-32-6.jpg?t=%E6%95%B0%E5%88%97%E9%A2%98%E4%B8%80%E9%81%93%2C%E5%85%B7%E4%BD%93%E8%A7%81%E5%9B%BE%E5%A6%82%E5%9B%BE%E6%89%80%E7%A4%BA)
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数列题一道,具体见图如图所示
数列题一道,具体见图
如图所示
数列题一道,具体见图如图所示
关健在于分析通项,根号里=
1+(1/n)^2+[1/(n+1)]^2
=[1/n-1/(n+1)]^2+2/n*(n+1)+1
={1/[n*(n+1)]}^2+2/n*(n+1)+1
={1/[n*(n+1)]+1}^2
S=1/1*2+1/2*3+...+1/2008*2009+2008
=(1/1-1/2)+(1/2-1/3)+...+(1/2008-1/2009)+2008
=1-1/2009+2008=2009-1/2009
[S]=2008