If `a_1,a_2,a_3,...,a_(n+1)` are in A.P. , then `1/(a_1a_2)+1/(a_2a_3)....+1/(a_na_(n+1))` is

If the nonzero numbers a_1,a_2,a_3,....,a_n are in AP, prove that 1/(a_1a_2a_3)+1/(a_2a_3a_4)+...+1/(a_(n-2)a_(n-1)a_n)=1/(2(a_2-a_1))(1/(a_1a_2)-1/(a_(n-1)a_n)) .

If a_1,a_2,a_3,.....,a_n are in AP, prove that 1/(a_1a_2)+1/(a_2a_3)+1/(a_3a_4)+...+1/(a_(n-1)a_n)=(n-1)/(a_1a_n) .

If a_1, a_2, a_3, .... a_4001 are terms of an A.P. such that 1/(a_1a_2)+1/(a_2a_3)+1/(a_3a_4)+......1/(a_4000a_4001)=10 and a_2+a_4000=50, then |a_1-a_4001| is equal to

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

Let r be the common ratio of the GP a_1,a_2,a_3,....,a_n . Show that 1/(a_1^m+a_2^m)+1/(a_2^m+a_3^m)+....+1/(a_(n-1)^m+a_n^m)=(1-r^((1-n)m))/(a_1^m(r^m-r^-m)) .

Let a_1,a_2,a_3 …. a_n be in A.P. If 1/(a_1a_n)+1/(a_2a_(n-1)) +… + 1/(a_n a_1) = k/(a_1 + a_n) (1/a_1 + 1/a_2 + …. 1/a_n) , then k is equal to :

"If "a_1,a_2,a_3,.....,a_n" are in AP, prove that "a_(1)+a_(n)=a_(r)+a_(n-r+1)""

If a_1,a_2,a_3,………….a_12 are in A.P. and /_\_1 =|(a_1a_5, a_1,a_2),(a_2a_6,a_2,a_3),(a_3a_7,a_3,a_4)|, |(a_2a_10, a_2,a_3),(a_3a_11,a_3,a_4),(a_4_12,a_4,a_5)| then /_\_1:/_\_2= (A) 1:2 (B) 2:1 (C) 1:1 (D) none of these