Example of a sequence needed that satisfies certain conditions Can you please provide examples of sequence $\{a_1,a_2,\cdots\}$ such that $\sum_{i=1}^{\infty}a_i\to \infty$ while $\sum_{i=1}^{\infty}(a_i)^2<\infty$ with each $a_i\in[0,1)$. Thank you.

An interesting one is an = $\frac{1} p_{n}$, where pn is the n'th prime. Then $\sum_{}^{} \frac{1} p_{n}$ diverges and $\sum_{}^{} \frac{1}p_{n}^2 $ converges by comparison to the reciprocals of squares. 
