Lp space and sequence For what value of $p$ the sequence $\displaystyle x_{n}=\frac{1}{n}$ is on $l^p$ (where $\displaystyle l^p = \lbrace (x_1,x_2,...)| x_{i}\in\mathbb{C}\hspace{0.1cm}\text{and}\hspace{0.1cm} \left(\sum_{i=1}^{\infty}|x_{i}|^p\right)^{1/p}<\infty\rbrace$).

If p=1, the series diverge. If p>2 it converges, so $x_n \in l^p$ for all $p\ge 2$ (since $l^p \subset l^{p+1}$)
