Let a1,a2,a3,a4...an 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 so much!
By Cauchy-Schwarz, the maximum value is n^2/4.