Answer to Question #159448 in Calculus for Vishal

Question

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 +∞

Answer 1

As there is no indeterminate form

$$\lim_{n\rightarrow+\infty}(a_n+b_n)=\lim_{n\rightarrow+\infty}a_n+\lim_{n\rightarrow+\infty}b_n=+\infty+\infty=+\infty,$$

and

$$\lim_{n\rightarrow+\infty}(a_n\cdot b_n)=\lim_{n\rightarrow+\infty}a_n\cdot\lim_{n\rightarrow+\infty}b_n=+\infty\cdot+\infty=+\infty.$$