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# Is convergent sequence always bounded?

- Is convergent sequence always bounded?
- Can a sequence converge and not be bounded?
- Is every sequence bounded?

## Is convergent sequence always bounded?

Theorem 1 (Theorem 9.1). Every convergent sequence is bounded.

## Can a sequence converge and not be bounded?

If a sequence is not bounded, it is an unbounded sequence. For example, the sequence 1/n is bounded above because 1/n≤1 for all positive integers n. It is also bounded below because 1/n≥0 for all positive integers n. Therefore, 1/n is a bounded sequence.

## Is every sequence bounded?

Proof: Every sequence in a closed and bounded subset is bounded, so it has a convergent subsequence, which converges to a point in the set because the set is closed.

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## How do I get a Gmail name that's already taken?

Originally Answered: how do I get an email address that is already taken? You can't - the only other option is to try a different email provider. But Gmail, for example, won't let you have the same email address as another person. An email address is similar to a postal address.

## How do you use quotes in Gmail?

Reply to an email using Quotes Open Gmail, and copy the part of the email you want to reply to. This adds a gray bar, marking where you quote the original message. Next to the gray bar, paste the original message text. Press Enter and enter your response below the original message.

## Why is Gmail continually syncing?

Check Storage So if your phone is running out of storage space, Gmail sync won't work or will get stuck at syncing. Open Settings > Device care > Storage to check how much space you have left. Go deeper into storage space settings to understand which file type is consuming the most space and where you can cut back.

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