Solveeit Logo
Login

Question

Question: If f(n + 1) = \(\frac { 1 } { 2 }\) \(\left\{ f(n) + \frac{9}{f(n)} \right\}\), n ∈ N and f(n) \> 0 ...

If f(n + 1) = 12\frac { 1 } { 2 } {f(n)+9f(n)}\left\{ f(n) + \frac{9}{f(n)} \right\}, n ∈ N and f(n) > 0 for all n ∈ N then lim⁡n→∞\lim_{n \rightarrow \infty}f(n) is equal to-

A

3

B

–3

C

½

D

None of these

Answer

3

Explanation

Solution

As n → ∞ . lim⁡n→∞\lim _ { n \rightarrow \infty } f(n) = lim⁡n→∞\lim _ { n \rightarrow \infty } f(n + 1) = k say

We have f(n + 1) = 12\frac { 1 } { 2 } (f(n)+9f(n))\left( \mathrm { f } ( \mathrm { n } ) + \frac { 9 } { \mathrm { f } ( \mathrm { n } ) } \right) or f(n)

= f(n + 1) = 12\frac { 1 } { 2 }

⇒ k = 12\frac { 1 } { 2 } ⇒ k2 = 9 or k = 3

∴ f (n) = 3.