Question

State and prove the following theorem
1)- comparison test

Answer 1

Answer:

Hint: Suppose that L>0 (a similar argument will deal with L<0).

Because limn→∞anbn=L, there is an N such that if n>N then

L2<anbn<3L2.

The above inequality follows from the definition of limit by taking ϵ=L2.

Now, as you expected, Comparison does it.