Thread: Using the Sandwich Theorem

Suppose that the sequence (a_n) converges to 0 and (b_n) is bounded. Use the Sandwich Theorem to prove that (a_n)(b_n) converges to 0.

I know that, since (b_n) is bounded, it is convergent to a limit L. But I'm not sure how to use the Sandwich Theorem to prove the product converges to 0 - any help would be greatly appreciated!

Originally Posted by sakuraxkisu

Suppose that the sequence (a_n) converges to 0 and (b_n) is bounded. Use the Sandwich Theorem to prove that (a_n)(b_n) converges to 0.
I know that, since (b_n) is bounded, it is convergent to a limit L. But I'm not sure how to use the Sandwich Theorem to prove the product converges to 0 - any help would be greatly appreciated!

That is a false claim.

It is true that such that

If then .

Now you finish.

Hi, thank you for your reply. Sorry about the mistake! I was wondering, would you perhaps be able to explain how the Sandwich Theorem can be used to prove this? Thanks

Originally Posted by sakuraxkisu

Hi, thank you for your reply. Sorry about the mistake! I was wondering, would you perhaps be able to explain how the Sandwich Theorem can be used to prove this?

There is no reason to use the Sandwich Theorem.
If you must, I don't see right now.

Originally Posted by sakuraxkisu

I was wondering, would you perhaps be able to explain how the Sandwich Theorem can be used to prove this?

Consider and where for all n. Show that .