已知數列{an}的通項公式an=n-根號下（1+n^2)判斷數列{an}的單調性
熱心網友
已知數列{an}的通項公式an=n-√(1+n^2)判斷數列{an}的單調性 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)]當n增大時,n+√(1+n^2)減小,1/[n+√(1+n^2)]增大,-1/[n+√(1+n^2)]減小.數列{an}是單調遞減的.
已知數列{an}的通項公式an=n-根號下（1+n^2)判斷數列{an}的單調性
已知數列{an}的通項公式an=n-√(1+n^2)判斷數列{an}的單調性 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)]當n增大時,n+√(1+n^2)減小,1/[n+√(1+n^2)]增大,-1/[n+√(1+n^2)]減小.數列{an}是單調遞減的.