# Thread: Here are two question to be proved...

1. ## 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:
$1/(b-a) + 1/(b-c) =1/c +1/a$

and one more....

Q. If n HM's(H1, H2, H3, H4......Hn) are inserted between a and b, then prove that:
$(H1+a)/(H1-a) +(Hn+b)/(Hn-b) = 2n$

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

2. In your case for question 1 the harmonic mean

$b = \frac{2}{\frac{1}{a}+\frac{1}{c}}$

3. also the special case for 2 numbers

$b = \frac{2ac}{a+c}$

4. for $1/(b-a) + 1/(b-c) =1/c +1/a$

substitute

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

Hopefully your result will be

1/c +1/a

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# if H1,H2,....Hn be n harmonic means between a and b then H1 a/H1-a Hn b/Hn-b is

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