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`

Let the sequence ltb_(n)gt of real numbers satisfy the recurrence relation b_(n+1)=1/3(2b_(n)+(125)/(b_(n)^(2))),b_(n)ne0. Then find lim_(ntoo0) b_(n).

If the geometric mean of a and b is (a^(n+1)+b^(n+1))/(a^(n)+b^(n)) then n = ?

If there are three square matrix A, B, C of same order satisfying the equation A^2=A^-1 and B=A^(2^n) and C=A^(2^((n-2)) , then prove that det .(B-C) = 0, n in N .

Let a and b be two positive unequal numbers , then (a^(n+1)+b^(n+1))/(a^(n)+b^(n)) represents

Let A = [(1,0),(2,3)] and A^(n) = [(a, b),(c,d)] then lim_(n to oo) (b + c)/(a + d) =

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

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

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

For what value of n , (a ^(n +3) + b ^(n +3))/(a ^(n +2) + b ^(n +2)), a ne b in the A.M. of a and b.

If a, a_1 ,a_2----a_(2n-1),b are in A.P and a,b_1,b_2-----b_(2n-1),b are in G.P and a,c_1,c_2----c_(2n-1),b are in H.P (which are non-zero and a,b are positive real numbers), then the roots of the equation a_nx^2-b_nx |c_n=0 are (a) real and unequal (b) real and equal (c) imaginary (d) none of these