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tnocel1
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Homework Statement
Show that if bn→b, then the sequence of absolute values |bn| converges to |b|.
Homework Equations
The Attempt at a Solution
I've been proving various properties of limits, including product of limits and sum of products, but have been having trouble making progress with the approach to absolute value of limits. I was also wondering is the converse of this is true, that is if |bn|→|b|, is it also true that (bn)→b