i want to show
1/(n^2) <= (a1^2) + (a2^2) + (a3^2) + ..... + (an^2)
given that a1 + a2 + .... + an =1
any idears
thankss
ok so let F = (a1^2) + (a2^2) + (a3^2) + ..... + (an^2) + y( a1 + ... + an -1)
df/dai = 2ai +y = 0
ai= -y/2
df/dfy = a1 + ... + an -1 =0
so y= -2/n so
ai = 1/n maxamises the (a1^2) + (a2^2) + (a3^2) + ..... + (an^2) so maximum is n*(1/n^2) =1/n
and 1/(n^2) < 1/n
thanks