IfÂ infinityÂ sigmaÂ n=1Â AnÂ beÂ aÂ convergentÂ seriesÂ thenÂ limitÂ x->Â infinityÂ AnÂ isÂ equalÂ to:

a)Â 0Â b)Â 1Â c)Â infinityÂ d)NoneÂ ofÂ these

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If `sum_(n=1)^(oo)A_n` is a convergent series, then `lim_(n->oo)A_n=?` :

**The answer is (a) zero**

If a series is convergent, then the limit of the underlying sequence must be zero. Note that the converse is true; a sequence whose nth term tends to zero need not have a convergent series.

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