Let `a_1=1`, `a_n=n(a_(n-1)+1` for `n=2,3,...` where `P_n=(1+1/a_1)(1+1/a_2)(1+1/a_3)....(1+1/a_n)` then `Lt_(nrarroo)P_n=`

Let a_(1)=1,a_(n)=n(a_(n-1)+1 for n=2,3,... where P_(n)=(1+(1)/(a_(1)))(1+(1)/(a_(2)))(1+(1)/(a_(3)))...*(1+(1)/(a_(n))) then Lt_(n rarr oo)P_(n)=

If 1, a_1,a_2,a_3 ,…, a_(n-1) are the nth roots of unity then prove that : (1-a_1)(1-a_2)(1-a_3)...(1-a_(n-1)) =n.

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_(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_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_i>0, i=1, 2, 3,..., n then prove that a_1/a_2+a_2/a_3+a_3/a_4+...+a_(n-1)/a_n+a_n/a_1gen .

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 :

Let (a_1,a_2,a_3....a_4) be a permutation of (1,2,3....n) for which a_1 > a_2 .a_3 >.........> a_ (a/2) and a_(n/2=1) a_2 >a_3..........>a_((x-2)/2 and a_((n-1)/2 <.... < a_2for n as positive integers. Let the total number of permutation of n be p(n). if 200 < p(n) < 5000. then values of n is /are

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 :-