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Series

Bwave
in Analysis and Calculus

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I was wondering what the rules are for a series to converge or not. In my calculus class our professor said that if it is bounded and monotonic then it will converge, but what are all the rules or characteristics a sequence must have?

Is there not really only one rule, that being the existence a limit?

I was wondering what the rules are for a series to converge or not. In my calculus class our professor said that if it is bounded and monotonic then it will converge, but what are all the rules or characteristics a sequence must have?

 

The rule you gave is for a sequence to converge, not for a series. Also a sequence may converge if it is not monotonic.

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