To determine the example of a series such that the partial sums S, are bounded but the series . k diverges.
Provide an example of a series
[tex]\Sigma^{\infty}_{k=1}[/tex]such that the partial sum Sn are bounded but the series
[tex]\Sigma^{\infty}_{k=1}a_{k\text{ }}\text{diverge}[/tex]Provide an example of a geometric series
[tex]\Sigma^{\infty}_{k=0}r^k[/tex]such that
[tex]\Sigma^{\infty}_{k=0}r^k\ne\frac{1}{1-r}[/tex]Provide an example of a series
[tex]\Sigma a_k[/tex]such that
[tex]\Sigma a_k[/tex]diverges but
[tex]\lim _{k\to\infty}a_k=0[/tex]