Question

A particle begins at the origin and moves 2 units to right and reaches P₁ then 1 unit up and reaches P₂, 1/2 unit right and reaches P₃, $\frac{1}{4}$ unit down to reach P₄& 1/8 unit right to reach
P₅ and so on. If P_n = (x_n, y_n) then $\lim_{n \rightarrow \infty}$ P_n is

• A. (4, 6)
• B. (8/3, 4/5)
• C. (4/5, 2)
• D. (4, 3)

Answer 1

Answer: (B)

(8/3, 4/5)

Answer 2

$\lim_{n \rightarrow \infty}$ x_n = $\frac{2\left( 1 - \left( \frac{1}{4} \right)^{n} \right)}{1 - \frac{1}{4}}$= 8/3

$\lim_{n \rightarrow \infty}$ y_n = $\frac{1\left( 1 - \left( \frac{- 1}{4} \right)^{n} \right)}{1 - \left( \frac{- 1}{4} \right)}$ = 4/5

⇒ (8/3, 4/5)