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Show that in A.P. the sum of two terms e...

Show that in A.P. the sum of two terms equidistant from the begining and end is constant. Hence. Prove that
`(1)/(x_(1)x_(n))+(1)/(x_(2)x_(n-1))+(1)/(x_(3)x_(n-2))+...+(1)/(x_(n-1)x_(2))+(1)/(x_(n)x_(1))=(2)/(x_(1)+x_(n))((1)/(x_(1))+(1)/(x_(2))+(1)/(x_(3))+...+(1)/(x_(n)))`
where `x_(1),x_(2),x_(3),..x_(n)` are in A.P.

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