If `a_n>1` for all `n in N` then `log_(a_2) a_1+log_(a_3) a_2+.....log_(a_1)a_n` has the minimum value of

If a_ngt1 for all ninN ,then log_(a_2)a_1+log_(a3)a_2+.....+log_(an)a_(n-1)+log_(a1)a_n has the minimum value

If a_1, a_2, a_3..... a_n in R^+ and a_1.a_2.a_3.........a_n = 1, then minimum value of (1+a_1 + a_1^2) (1 + a_2 + a_2^2)(1 + a_3 + a_3^2)........(1+ a_n + a_n^2) is equal to :-

If a_1, a_2, a_3,.....a_n are in H.P. and a_1 a_2+a_2 a_3+a_3 a_4+.......a_(n-1) a_n=ka_1 a_n , then k is equal to

If a_1, a_2, a_3,.....a_n are in H.P. and a_1 a_2+a_2 a_3+a_3 a_4+.......a_(n-1) a_n=ka_1 a_n , then k is equal to

If a_1, a_2, a_3,.....a_n are in H.P. and a_1 a_2+a_2 a_3+a_3 a_4+.......a_(n-1) a_n=ka_1 a_n , then k is equal to

We know that, if a_1, a_2, ..., a_n are in H.P. then 1/a_1,1/a_2,.....,1/a_n are in A.P. and vice versa. If a_1, a_2, ..., a_n are in A.P. with common difference d, then for any b (>0), the numbers b^(a_1),b^(a_2),b^9a_3),........,b^(a_n) are in G.P. with common ratio b^d. If a_1, a_2, ..., a_n are positive and in G.P. with common ration, then for any base b (b> 0), log_b a_1 , log_b a_2,...., log_b a_n are in A.P. with common difference logor.If x, y, z are respectively the pth, qth and the rth terms of an A.P., as well as of a G.P., then x^(z-x),z^(x-y) is equal to

If a_i > 0 for i=1,2,…., n and a_1 a_2 … a_(n=1) , then minimum value of (1+a_1) (1+a_2) ….. (1+a_n) is :

If a_i > 0 for i=1,2,…., n and a_1 a_2 … a_(n=1) , then minimum value of (1+a_1) (1+a_2) ….. (1+a_n) is :

{a_n} and {b_n} are two sequences given by a_n=(x)^(1//2^n) +(y)^(1//2^n) and b_(n)=(x)^(1//2^n)-(y)^(1//2^n) for all n in N. The value of a_1 a_2 a_3……..a_n is equal to