1

why $$ \underset{n\rightarrow \infty}{\lim}\left( \frac{1}{n+1}+\cdot \cdot \cdot +\frac{1}{2n} \right) =\underset{n\rightarrow \infty}{\lim}\frac{1}{n+1}+\cdot \cdot \cdot +\underset{n\rightarrow \infty}{\lim}\frac{1}{2n}=0 $$ is wrong?

Alan Muniz
  • 4,964
user142088
  • 25
  • 1
    This fails as the number of terms is not finite. We need to use https://math.stackexchange.com/questions/469885/the-limit-of-a-sum-sum-k-1n-fracnn2k2 – lab bhattacharjee Nov 27 '19 at 09:38
  • 3
    Isn't it obvious? The number of terms in the first limit is going to infinity. Suppose each term was $1/n$. Then their sum would always be 1, but each term would go to zero. – almagest Nov 27 '19 at 09:39
  • thank you very much. – user142088 Nov 27 '19 at 09:56

0 Answers0