Arithmetic progression problem? asked this question 3 times no proper answers yet. can anyone solve this.?

Question

prove that
1/a1an + 1a2an-1 + 1/a3an-2 + .................. + 1an-1a2 + 1/ana1 = 2/a1+an(1/a1+1/a2+.......1/an)

here 'a1' means first term 'a2' second and similarly 'an-1' second last and 'an' last.
please help. thank you

where are the top contributers

Answer 1

If I'm interpreting what you wrote correctly, then you can't prove it because it is not true. This is easily shown with an example.

What you have written can be put in summation notation as:

Sum {(i = 1 to n) of ((a_i*a_(n-i+1))^(-1^i)} = 2/a_1 + a_n*Sum{(j = 1 to n) of 1/a_j}

For instance, take the two-term arithmetic progression: 1,2

Plug this into your "equation":

1/(1*2) + 2*1 = 2/1 + 2*(1/1 + 1/2)

2.5 = 5, which is obviously incorrect, so your hypothesis (if I'm reading it correctly) is also false.

Answer 2

I think there are too many ambiguities. Retype with rigorous use of parentheses.

Answer 3

use more brackets to make the expression clear.