# Here are two question to be proved...

• May 26th 2009, 08:57 PM
findmehere.genius
Here are two question to be proved...
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.
• May 26th 2009, 11:16 PM
pickslides
In your case for question 1 the harmonic mean

$\displaystyle b = \frac{2}{\frac{1}{a}+\frac{1}{c}}$
• May 26th 2009, 11:19 PM
pickslides
also the special case for 2 numbers

$\displaystyle b = \frac{2ac}{a+c}$
• May 28th 2009, 09:03 PM
pickslides
for $\displaystyle 1/(b-a) + 1/(b-c) =1/c +1/a$

substitute

$\displaystyle b = \frac{2}{\frac{1}{a}+\frac{1}{c}}$ into the left hand side $\displaystyle 1/(b-a) + 1/(b-c)$ and simplify...