Home
Class 12
MATHS
Let the sequence {bn} real numbers satis...

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`

Text Solution

Verified by Experts

The correct Answer is:
5
Let `underset(ntooo)limb_(n)=b`
Now `b_(n+1)=1/3(2b_(n)+(125)/(b_(n)^(2)))`
`implies" "underset(ntooo)limb_(n+1)=1/3(2underset(ntooo)limb_(n)+(125)/(underset(ntooo)limb_(n)^(2)))`
`implies" "b=1/3(2b+(125)/(b^(2)))" "( :.underset(ntooo)limb_(n)=underset(ntooo)limb_(n+1)=b)`
`implies" "b/3=(125)/(3b^(2))`
`implies" "b^(3)=125`
`implies" "b=5`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE|Exercise Exercise 2.3|15 Videos

  • LIMITS

    CENGAGE|Exercise Exercise 2.4|5 Videos

  • LIMITS

    CENGAGE|Exercise Exercise 2.1|10 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

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) ?