Give an example of a series ∑an such that ∑an is not convergent but the sequence (an) converges to 0.
Consider the harmonic series
The sequence {an}\{a_n\}{an} defined by an=1n,n≥1a_n=\dfrac{1}{n}, n\geq1an=n1,n≥1 converges to 0.0.0.
But the series ∑i=1n1n\displaystyle\sum_{i=1}^n\dfrac{1}{n}i=1∑nn1 is divergent.
Need a fast expert's response?
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS!
Comments
Leave a comment