求救：看得懂英文版高等数学的数学高手请进.(TheSandwichTheorem)Giventwoconvergentsequences{an}and{cn}withthesamelimitlimn->∞an=L=limn->∞cn.Let{bn}beasequence.Supposethereexistsapositiveinteg

Question

求救：看得懂英文版高等数学的数学高手请进.
(The Sandwich Theorem)Given two convergent sequences {an} and {cn} with the same limit lim n->∞ an = L = lim n->∞ cn.Let {bn} be a sequence.Suppose there exists a positive integer K such that for n ≥ K,we have an ≤ bn ≤ cn.Then bn converges to L.


Answer 1

【比较定理】给定两个收敛的序列{an} 和{cn} ,它们的n值趋于无穷大,an = L = lim n->∞ cn. {bn}也是一个序列.假定存在一个正整数K满足n>=k
时,我们得到an ≤ bn ≤ cn. 那么bn收敛于L