求 证Lim ( n/ n2+1) + (n/ n2+2) +( n/ n2+3).+(n/n2+n)当n趋向无穷时的极限为1
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![求 证Lim ( n/ n2+1) + (n/ n2+2) +( n/ n2+3).+(n/n2+n)当n趋向无穷时的极限为1](/uploads/image/z/3395256-24-6.jpg?t=%E6%B1%82+%E8%AF%81Lim+%28+n%2F+n2%2B1%29+%2B+%28n%2F+n2%2B2%29+%2B%28+n%2F+n2%2B3%29.%2B%28n%2Fn2%2Bn%29%E5%BD%93n%E8%B6%8B%E5%90%91%E6%97%A0%E7%A9%B7%E6%97%B6%E7%9A%84%E6%9E%81%E9%99%90%E4%B8%BA1)
求 证Lim ( n/ n2+1) + (n/ n2+2) +( n/ n2+3).+(n/n2+n)当n趋向无穷时的极限为1
求 证Lim ( n/ n2+1) + (n/ n2+2) +( n/ n2+3).+(n/n2+n)当n趋向无穷时的极限为1
求 证Lim ( n/ n2+1) + (n/ n2+2) +( n/ n2+3).+(n/n2+n)当n趋向无穷时的极限为1
用夹逼定理即可:
设原极限为I:
lim(n/(n^2+1))*n
放缩一下很容易看出:
n^2/(n^2+n) < 原式 < n^2/(n^2+1)
两边极限都是1