Let $a_1,$ $a_2,$ $\dots,$ $a_n$ be real numbers such that
\[a_1^2+2a_2^2+\cdots+na_n^2 = 1.\]Find the maximum value of $(a_1+2a_2+\cdots+na_n)^2.$
Thanks,
By Cauchy-Schwarz, the maximum value is 1/n^2.
1/n^2 isn't correct
