Example to the statement that $a_{n+1} - a_n \rightarrow 0$ as $n \rightarrow \infty$ does not imply that sequence $a_n$ converges. [duplicate]
Solution 1:
How about $a_n=\sum_{k=1}^{n}\frac{1}{k}.$
Example to the statement that $a_{n+1} - a_n \rightarrow 0$ as $n \rightarrow \infty$ does not imply that sequence $a_n$ converges. [duplicate]
Solution 1:
How about $a_n=\sum_{k=1}^{n}\frac{1}{k}.$