已知数列{an}的通项公式an=n-根号下（1+n^2)判断数列{an}的单调性
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已知数列{an}的通项公式an=n-√(1+n^2)判断数列{an}的单调性 an=n-√(1+n^2)=[n-√(1+n^2)][n+√(1+n^2)]/[n+√(1+n^2)]=n^2-(1+n^2)]/[n+√(1+n^2)]=-1/[n+√(1+n^2)]当n增大时,n+√(1+n^2)减小,1/[n+√(1+n^2)]增大,-1/[n+√(1+n^2)]减小.数列{an}是单调递减的.
已知数列{an}的通项公式an=n-根号下（1+n^2)判断数列{an}的单调性
已知数列{an}的通项公式an=n-√(1+n^2)判断数列{an}的单调性 an=n-√(1+n^2)=[n-√(1+n^2)][n+√(1+n^2)]/[n+√(1+n^2)]=n^2-(1+n^2)]/[n+√(1+n^2)]=-1/[n+√(1+n^2)]当n增大时,n+√(1+n^2)减小,1/[n+√(1+n^2)]增大,-1/[n+√(1+n^2)]减小.数列{an}是单调递减的.