If `a_1,a_2,a_3….a_(2n+1)` are in A.P then
`(a_(2n+1)-a_1)/(a_(2n+1)+a_1)+(a_2n-a_2)/(a_(2n)+a_2)+....+(a_(n+2)-a_n)/(a_(n+2)+a_n)` is equal to

If a_1,a_2,….a_n are in H.P then (a_1)/(a_2+,a_3,…,a_n),(a_2)/(a_1+a_3+….+a_n),…,(a_n)/(a_1+a_2+….+a_(n-1)) are in

If a_(1), a_(2) , ……. A_(n) are in H.P., then the expression a_(1)a_(2) + a_(2)a_(3) + ….. + a_(n - 1)a_(n) is equal to

If a_1,a_2,a_3…a_n are in H.P and f(k)=(Sigma_(r=1)^(n) a_r)-a_k then a_1/f(1),a_2/f(3),….,a_n/f(n) are in

If a_(1), a_(2), a_(3), ……. , a_(n) are in A.P. and a_(1) = 0 , then the value of (a_(3)/a_(2) + a_(4)/a_(3) + .... + a_(n)/a_(n - 1)) - a_(2)(1/a_(2) + 1/a_(3) + .... + 1/a_(n - 2)) is equal to

If a_1, a_2, ,a_n >0, then prove that (a_1)/(a_2)+(a_2)/(a_3)+(a_3)/(a_4)++(a_(n-1))/(a_n)+(a_n)/(a_1)> n

If A_(1), A_(2),..,A_(n) are any n events, then

If a_(1), a_(2), a_(3), ......... , are in A.P. with common difference 5 and if a_(i)a_(j) != - 1 for i ,j = 1, 2, .... , n , then tan^(1)(5/(1 + a_(1) a_(2))) + tan ^(1)(5/(1 + a_(2)a_(3))) + ...... + tan^(-1)(5/(1 + a_(n - 1)a_(n))) is equal to

If the sequence a_(1),a_(2),a_(3),…,a_(n) is an A.P., then prove that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+…+a_(2n-1)^(2)-a_(2n)^(2)=n/(2n-1)(a_(1)^(2)-a_(2n)^(2))

Let a_1,a_2,a_3…., a_49 be in A.P . Such that Sigma_(k=0)^(12) a_(4k+1)=416 and a_9+a_(43)=66 .If a_1^2+a_2^2 +…+ a_(17) = 140 m then m is equal to