If a1, a2, a3, …, an-1 are in arith. progression, prove that 1/(a1 an) + 1/(a2 an-1) + 1/(a3 an-2) + ... +1/(an a1) = (1/a1 + 1/a2 + ... +

[babulkar]

If a1 , a2 , a3 …….. an-1 , an are in arithmetic progression prove that
1/(a1 an) + 1/( a2 an-1) + 1/ (a3 an-2) +………….+1/(an a1) =
(1/a1 + 1/a2 + 1/ a3 +……..1/an ) X { 2/(a1 +an)}

 

[MarkFL]

Hello, and welcome to FMH!

Can you show what you done so far so we may better know how to help?

 

[babulkar]

I am not able to solve it . can you help me

 

[JeffM]

Did you try a proof by induction?

 

[babulkar]

no

 

[MarkFL]

no

Like Jeff, my first inclination was to try a proof by induction. Are you familiar with the method?

 

[babulkar]

yes i am trying

 

[Dr.Peterson]

Another approach you might take is to multiply the LHS by (a_1 +a_n)/2, keeping in mind that a_1 + a_n = a_2 + a_{n-1} = ... . Each term will simplify interestingly.

 

[Steven G]

I understand that you can't do this problem but that doesn't mean you can't do anything. Show us something and we'll help you go further.

 

[babulkar]

Dr Peterson's approach to multiply the LHS by (a_1 +a_n)/2, keeping in mind that a_1 + a_n = a_2 + a_{n-1} = helped me solving the problem. Thanks all for your help.