If H1,H2,H3.........H20 be 20 harmonic means between 2 and 3 then H1+2/H1-2 + H20+3/H20-3=????

We know that,
13=12+21d⇒d=−16×21     ⋯(1)
Now, given 
H1+2H1−2+H20+3H20−3=12+1H112−1H1+13+1H2013−1H20
=12+12+d12−d−12+13+13−d13−13+d(∵1H1=12+d,  1H20=13−d)
=1+d−d+23−dd=23−d−1−dd=−13−2dd=−13d−2
=6×213−2=40   [Using equation (1)]