Well, I began with Harmonic Progression yesterday....and no sooner did I start I met with this Olympus like question(thats just for me).....maybe anyone likes to help.

Q. If b be the harmonic mean(HM) between a and c, then prove:

$\displaystyle 1/(b-a) + 1/(b-c) =1/c +1/a $

and one more....

Q. If n HM's(H1, H2, H3, H4......Hn) are inserted between a and b, then prove that:

$\displaystyle (H1+a)/(H1-a) +(Hn+b)/(Hn-b) = 2n$

I will be thankful if I cross the olympus...with anyone's help.