WBJEE · Maths · Sequences and Series
A particle starts at the origin and moves l unit horizontally to the right and reaches \(P_{1}\), then it moves \(\frac{1}{2}\) unit vertically up and 2 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 \(P_{\mathrm{S}}\) and so on. Let \(P_{n}=\left(x_{n}, y_{n}\right)\) and \(\lim _{n \rightarrow \infty} x_{n}=\alpha\) and \(\lim _{n \rightarrow \infty} y_{n}=\beta .\) Then, \((\alpha, \beta)\) is
- A (2,3)
- B \(\left(\frac{4}{3}, \frac{2}{5}\right)\)
- C \(\left(\frac{2}{5}, 1\right)\)
- D \(\left(\frac{4}{3}, 3\right)\)
Answer & Solution
Correct Answer
(B) \(\left(\frac{4}{3}, \frac{2}{5}\right)\)
Step-by-step Solution
Detailed explanation
According to the given information in question, we can draw the situation of particle at different stages as following Here, \(x_{1}=1, x_{2}=1, x_{3}=\frac{5}{4}, x_{4}=\frac{5}{4}\) and \(x_{5}=\frac{21}{16}\)…
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