Answer to Question #159448 in Calculus for Vishal

Question #159448

Let {an}∞n=1 and {bn}∞n=1 be sequences both of which diverge to +∞. Then both of {an +bn}∞n=1 and {an · bn}∞n=1 diverge to +∞


1
Expert's answer
2021-02-02T05:28:10-0500

As there is no indeterminate form

limn+(an+bn)=limn+an+limn+bn=++=+,\lim_{n\rightarrow+\infty}(a_n+b_n)=\lim_{n\rightarrow+\infty}a_n+\lim_{n\rightarrow+\infty}b_n=+\infty+\infty=+\infty,

and

limn+(anbn)=limn+anlimn+bn=++=+.\lim_{n\rightarrow+\infty}(a_n\cdot b_n)=\lim_{n\rightarrow+\infty}a_n\cdot\lim_{n\rightarrow+\infty}b_n=+\infty\cdot+\infty=+\infty.


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