专注交流，全球最倒霉的人帮你解疑答惑

专注交流，全球最倒霉的人帮你解疑答惑

2020年欧洲杯葡萄牙败北德国，最明显的原因是什么？

2020年欧洲杯并未举行，因此无法回答该问题。

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(1-1/2)+(1/2-1/3)+(1/3-1/4)+···+（1/2009-1/2010

To find the sum of the given series, we need to add all the terms together. (1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + ... + (1/2009 - 1/2010) We can simplify each term by finding the common denominator. 1 - 1/2 = 2/2 - 1/2 = 1/2 1/2 - 1/3 = 3/6 - 2/6 = 1/6 1/3 - 1/4 = 4/12 - 3/12 = 1/12 We can observe that each term follows this pattern - the denominator of the second fraction becomes the denominator of the first fraction in the next term. So, the series can be written as: 1/2 + 1/6 + 1/12 + ... + 1/2009 To find the sum of this series, we need to find the common denominator of all the fractions. The common denominator of 2, 6, 12, ..., 2009 will be the least common multiple (LCM) of these numbers. Calculating the LCM of these numbers is a bit lengthy. Instead, we can find the LCM of 2, 3, 4, ..., 2010, and then divide by the LCM of 2, 3, 4, ..., 2009. LCM(2, 3, 4, ..., 2010) / LCM(2, 3, 4, ..., 2009) = 2010 / 2 = 1005 So, the common denominator is 1005. To add the fractions, we need to express them with the common denominator: 1/2 = (1/2) * (1005/1005) = 1005/2010 1/6 = (1/6) * (1005/1005) = 167.5/2010 1/12 = (1/12) * (1005/1005) = 83.75/2010 Now we can add: 1005/2010 + 167.5/2010 + 83.75/2010 + ... + 1/2009 We can observe that the denominators of the fractions form an arithmetic sequence, and the numerators follow the same pattern. Using the formula for the sum of an arithmetic sequence: Sum = (first term + last term) * number of terms / 2 In this case, the first term is 1005/2010, the last term is 1/2009, and the number of terms is 2010. Sum = (1005/2010 + 1/2009) * 2010/2 Sum = (1005/2010 + 1/2009) * 1005 Sum = (1005 * 2009 + 1 * 2010) / 2 Sum = (2019955 + 2010) / 2 Sum = 2021965 / 2 Sum = 1010982.5 Therefore, the sum of the given series is 1010982.5.

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人为什么要睡觉！

人需要睡觉是因为睡眠对我们的身体和大脑功能有重要影响。以下是一些睡眠的重要作用： 1. 修复和恢复：睡眠是我们身体修复和恢复的过程。它有助于修复疲劳的肌肉、修复受伤的组织并恢复身体能量。 2. 促进健康：睡眠对于维持身体健康至关重要。充足的睡眠可以降低患心脏病、中风、糖尿病、肥胖等慢性疾病的风险。 3. 支持大脑功能：睡眠对大脑功能的发展和提高至关重要。它可以促进学习、记忆和创造力的提升，并对情绪稳定和注意力集中起着重要作用。 4. 免疫支持：睡眠对免疫系统的功能至关重要。充足的睡眠可以增强机体对抵御感染和疾病的能力。 5. 维持生理平衡：睡眠可以调节体内的生理平衡，包括体温、血压、血糖和激素水平等，以保持身体正常运行。 综上所述，睡眠对人类身体和大脑的健康至关重要，确保充足的睡眠可以提高生活质量，并预防许多健康问题。

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