Let the sequence ``real numbers satisfies the recurrence relation `b_(n+1)=1/3(2b_n+(125)/(b n2)),b_n!=0.`Then find the`("lim")_(nvecoo)b_ndot`

Let the sequence ``real numbers satisfies the recurrence relation `b_(

1.	Let the sequence ``real numbers satisfies the recurrence relation `b_(n+1)=1/3(2b_n+(125)/(b n2)),b_n!=0.`Then find the`("lim")_(nvecoo)b_ndot`
Answer» Correct Answer - C Let `lim_(nto oo)b_(n)=b`. Then, ` b_(n+1)=(1)/(3)(2b_n+(125))/(b_(n^(2))), b_(n) ne 0`, then, `lim_(nto oo) b_n=` then, `lim_(nto oo) b_n=` `rArr lim_(nto oo) b_(n+1)=(1)/(3) {2 lim_(nto oo) b_(n)+(125)/(lim_(nto oo) b_n^(2))}` ` rArr b=(1)/(3) {2b +(125)/(b^2)}` ` rArr (b)/(3)=(125)/(3b^2)rArr b^3=125rArr b=5`

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