Let the sequence `{b_n}` real numbers satisfies the recurrence relation `b_(n+1)=1/3(2b_n+(125)/(b_n)^2),b_n!=0.` Then find the `(lim)_(n to oo)b_ndot`

If log_(b) n = 2 and log_(n) 2b = 2 , then find the value of b.

Evaluate: lim_(n->oo)[1/(n a)+1/(n a+1)+1/(n a+2)++1/(n b)]

If a_(n) and b_(n) are positive integers and a_(n)+sqrt2b_(n)=(2+sqrt2))^(n) , then lim_(nrarroo) ((a_(n))/(b_(n))) =

If I_n=int_0^(sqrt(3))(dx)/(1+x^n),(n=1,2,3. .), then find the value of ("lim")_(n->oo)I_ndot (a)0 (b) 1 (c) 2 (d) 1/2

Find the value of n so that (a^(n+1)+b^(n+1))/(a^(n)+b^n) may be the geometric mean between a and b.

If n (A) =5 and n(B ) =7 , then the number of relations on A xx B is

Let a ,b ,a n dc be any three nonzero complex number. If |z|=1a n d' z ' satisfies the equation a z^2+b z+c=0, prove that a ( bara) =c (barc) a n d|a||b|=sqrt(a c( bar b )^2)

Let a and b be two real numbers such that a > 1, b > 1. If A=[(a,0), (0,b)] , then lim_(n to oo) A^(-n) is a. unit matrix b. null matrix c. 2l d. none of these

If (a^(n)+b^n)/ (a^(n-1) +b^(n-1)) is the A.M. between a and b, then find the value of n.

Write a general polynomial q(z) of degree n with coefficients that are b_(0),b_(1),b_(2), . . .. b_(n) , What are the conditions on b_(0),b_(1),b_(2), . . .. b_(n) ?