Question

Let the sequence < b_n> of real numbers satisfy the recurrence relation : $\frac{x^{3} + x^{2} - 16x + 20}{(x - 2)^{2}}$, b_n¹ 0, then $f(x) = \cos x - \sin x,$ is equal to –

• A. 0
• B. 
• C. 5
• D. $( - 1,1)$

Answer 1

Answer: (C)

5

Answer 2

Letb_n = b

Then, b_{n +1} = $\frac { 1 } { 3 }$

b_{n + 1} = $\frac { 1 } { 3 } \left( 2 \lim _ { n \rightarrow \infty } b _ { n } + \frac { 125 } { \lim _ { n \rightarrow \infty } b _ { n } ^ { 2 } } \right)$

Ž b = $\frac { 1 } { 3 }$ $\left( 2 b + \frac { 125 } { b ^ { 2 } } \right)$

Ž = $\frac { 125 } { b ^ { 2 } }$ Ž b³ = 125 Ž b = 5