标签:Mathematical infty right sequence Introduction Thinking limit tends Man
8.Prove that if the sequence {an}n=1∞ tends to limit L as n→∞, then for any fixed number M>0, the sequence {Man}n=1∞ tends to the limit ML.
Proof: Because the sequence {an}n=1∞ tends to limit L as n→∞, for any ϵ, we can find an m such that for all n⩾m, we have ∣an−L∣⩽ϵ.
Multiply both sides by M, so we have M∣an−L∣⩽Mϵ. By algebra, we have∣Man−ML∣⩽Mϵ, for any Mϵ.Therefore, the sequence {Man}n=1∞ tends to the limit ML.
标签:Mathematical,infty,right,sequence,Introduction,Thinking,limit,tends,Man 来源: https://blog.csdn.net/yuh_yeet/article/details/104144531
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