Suppose that {a_n} and {b_n} are two sequences with the properties lim_{n \\to \

Question

Suppose that {a_n} and {b_n} are two sequences with the properties lim_{n o infty} a_n = + infty and

lim_{n o infty} b_n = B, where B is finite. suppose that B is positive. Prove that lim_{n o infty} a_nb_n =

+infty. Warning: You can't use the Simple Limit Theorems for infinite limits, so you have to prove this by using the

definitions.

Suppose that and are two sequences with the properties an = + infinity and tn = B, where B is finite. Prove that (an - tn) = + infinity. * warning = You can't use the simple limit theorem for infinite limits, so you have to prove this by using the definitions.

Explanation / Answer

if B is +ve,(however small it is), taking infinity as 1/0, the procut becomes B/0.

so as B is +ve,product becomes infinity.(proved.

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