2000 Putnam A1

Let $A$ be a positive real number. What are the possible values of

$\sum_{j=0}^\infty x_j^2$, given that $x_0,x_1,\ldots$ are positive

numbers

for which $\sum_{j=0}^\infty x_j=A$?

令 $A$ 为正实数。可能的值有哪些

$\sum_{j=0}^\infty x_j^2$，假设 $x_0,x_1,\ldots$ 为正

数字

对于 $\sum_{j=0}^\infty x_j=A$？