How can I find a sequence of numbers $A_n \in \mathbb{R} $ (not infinitely many of them being zero) such that
$ \sum_{n=1}^{\infty} (-1)^{n-1} \cdot A_n = 1$
and
$ \sum_{n=1}^{\infty} (-1)^{n-1} \cdot \sqrt{\frac{1-n \cdot (A_n)^{2}}{n}} = 0 \space \space \space $ ?
( It is also required that the latter series doesn’t have infinitely many zeroes )