Evaluate `underset( n rarroo)("lim") ((a_(1) + 1)/( a_(1))) ((a_(2) +1)/(a_(2))) "......." ((a_(n) +1)/( a_(n)))` where ` a_(1) 1 ` and ` a_(n) = n ( 1+ a_(n-1) ) AA n ge 2`

Evaluate: lim_(n rarr oo)((a_(1)^((1)/(1))+a_(2)^((1)/(2))+...+a_(n)^((1)/(n)))/(n))^(nx)

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

Find a_(1) and a_(9) if a_(n) is given by a_(n) = (n^(2))/(n+1)

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)=

a1,a2,a3.....an are in H.P. (a_(1))/(a_(2)+a_(3)+ . . .+a_(n)),(a_(2))/(a_(1)+a_(3)+ . . . +a_(n)),(a_(3))/(a_(1)+a_(2)+a_(4)+ . . .+a_(n)), . . .,(a_(n))/(a_(1)+a_(2)+ . . . +a_(n-1)) are in

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