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بالمناسبه انا احب القصه و ساقوم بمتابعتها و لاكن أوضح انه لو كان يريد الاسترخاء حقاء لكان كسب نقطه واحده و انتظر هذا كل ما فى الامر

Here's the corrected and well-formatted English version: --- If you earn only 1 point on the first day and then stop working, but the points continue to double daily, the sequence follows this formula: P_n = P_0 \times 2^{(n-1)} Where: (initial points). is the number of days after the first day. We need to find such that: 2^{(n-1)} \geq 1000 As calculated earlier: n - 1 \geq \log_2(1000) \approx 9.97 Thus: n \geq 11 Conclusion: You will reach 1,000 points on day 11, even if you stop working after the first day!

the number of days required to reach 1,000 points if you start by earning 1 point per day, with the total points doubling daily, we use the following formula: P_n = P_0 \times 2^{(n-1)} Where: is the number of points on day . (initial points on the first day). is the number of days. The total points double each day. Finding the Required Number of Days We need to find the smallest such that: 2^{(n-1)} \geq 1000 Taking the logarithm on both sides: (n-1) \times \log_2(2) \geq \log_2(1000) Since , we get: n - 1 \geq \log_2(1000) Now, we calculate : \log_2(1000) = \frac{\log_{10}(1000)}{\log_{10}(2)} Given that and , we get: \log_2(1000) \approx \frac{3}{0.301} \approx 9.97 Thus: n - 1 \geq 9.97 n \geq 11 Conclusion: You will need approximately 11 days to reach 1,000 points.

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