If `a_(1), a_(2), a_(3),…, a_(n)` be in A.P. Show that,
`(1)/(a_(1)a_(2)) + (1)/(a_(2)a_(3)) +….+(1)/(a_(n-1)a_(n)) = (n-1)/(a_(1)a_(n))`

If a_(1) ge 0 for all t and a_(1), a_(2), a_(3),….,a_(n) are in A.P. then show that, (1)/(a_(1)a_(3)) + (1)/(a_(3)a_(5)) +...+ (1)/(a_(2n-1).a_(2n+1)) = (n)/(a_(1)a_(2n+1))

If a_(1), a_(2), a_(3), …., a_(n) are in H.P., prove that, a_(1)a_(2) + a_(2)a_(3) + a_(3)a_(4) +…+ a_(n-1)a_(n) = (n-1)a_(1)a_(n)

If a_(1), a_(2) , a_(3),…,a _(n+1) are in A. P. then the value of (1)/(a _(1)a_(2))+(1)/(a_(2)a_(3))+(1)/(a_(3)a_(4))+...+(1)/(a_(n)a_(n+1)) is-

If a_(1),a_(2),a_(3),,a_(n) are an A.P.of non-zero terms, prove that _(1)(1)/(a_(1)a_(2))+(1)/(a_(2)a_(3))++(1)/(a_(n-1)a_(n))=(n-1)/(a_(1)a_(n))

If a_(1),a_(2),a_(3),dots,a_(n+1) are in A.P.then (1)/(a_(1)a_(2))+(1)/(a_(2)a_(3))...+(1)/(a_(n)a_(n+1)) is

Let a_(1),a_(2),a_(3), . . .,a_(n) be an A.P. Statement -1 : (1)/(a_(1)a_(n))+(1)/(a_(2)a_(n-1))+(1)/(a_(3)a_(n-1))+ . . .. +(1)/(a_(n)a_(1)) =(2)/(a_(1)+a_(n))((1)/(a_(1))+(1)/(a_(2))+ . . .. +(1)/(a_(n))) Statement -2: a_(r)+a_(n-r+1)=a_(1)+a_(n)" for "1lerlen

Let a_(1),a_(2),a_(3), . . .,a_(n) be an A.P. Statement -1 : (1)/(a_(1)a_(n))+(1)/(a_(2)a_(n-1))+(1)/(a_(3)a_(n-1))+ . . .. +(1)/(a_(n)a_(1)) =(2)/(a_(1)+a_(n))((1)/(a_(1))+(1)/(a_(2))+ . . .. +(1)/(a_(n))) Statement -2: a_(r)+a_(n-r+1)=a_(1)+a_(n)" for "1lerlen

Let a_(1),a_(2),a_(3),...a_(n) be an AP.Prove that: (1)/(a_(1)a_(n))+(1)/(a_(2)a_(n-1))+(1)/(a_(3)a_(n-2))+......+(1)/(a_(n)a_(1))=