A particle starts at the origin and moves 1 unit horizontally to the right and reaches P1, then it moves 12 unit vertically up and reaches P2, then it moves 14 unit horizontally to right and reaches P3, then it moves 18 unit vertically down and reaches P4, then it moves 116 unit horizontally to right and reaches P5 and so on. Let Pn=(xn,yn) and limn→∞xn=α and limn→∞yn=β. Then (α,β) is

A particle starts at the origin and moves 1 unit horizontally to the r

1.	A particle starts at the origin and moves 1 unit horizontally to the right and reaches P1, then it moves 12 unit vertically up and reaches P2, then it moves 14 unit horizontally to right and reaches P3, then it moves 18 unit vertically down and reaches P4, then it moves 116 unit horizontally to right and reaches P5 and so on. Let Pn=(xn,yn) and limn→∞xn=α and limn→∞yn=β. Then (α,β) is
Answer» A particle starts at the origin and moves $1$ unit horizontally to the right and reaches $P_{1}$ , then it moves $\frac{1}{2}$ unit vertically up and reaches $P_{2}$ , then it moves $\frac{1}{4}$ unit horizontally to right and reaches $P_{3}$ , then it moves $\frac{1}{8}$ unit vertically down and reaches $P_{4}$ , then it moves $\frac{1}{16}$ unit horizontally to right and reaches $P_{5}$ and so on. Let $P_{n} = (x_{n}, y_{n})$ and $lim n \to \infty x_{n} = α$ and $lim n \to \infty y_{n} = β .$ Then $(α, β)$ is