Question: 1. Prove: If (an) and (bn) are bounded sequences, then the sequence (an+bn) is bounded. Hint: Triangle Inequality 2. . Give an example to show

1. Prove: If (an) and (bn) are bounded sequences, then the sequence (an+bn) is bounded. Hint: Triangle Inequality

2. . Give an example to show that it is possible for (an +bn) to be bounded while (an) and (bn) are unbounded. Note: This demonstrates that the converse of #1 is false!

3. Prove: If lim an = a and lim(an bn) = 0, then lim bn = a.

Note: You are not allowed to use the Limit Rules! You should use the , N-definition of limits instead.

Hint: Triangle Inequality

Hint: Think of an as a middle-man between bn and a.

Hint: an an is a clever version of 0 that might come in handy!

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