为什么谈恋爱越久就越难分手?知识星球平台,学习分享交流利器

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为什么谈恋爱越久就越难分手?知识星球平台,学习分享交流利器

发布时间:2025-05-24 09:38

时间:2025-05-24 09:38

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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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古代把二月二作为什么


古代把二月二作为祭祀龙神和祈求五谷丰收的重要节日。古人认为龙是中国的图腾,具有神圣的象征意义。二月二是龙和虫子活动的时候,所以被视为祭祀龙神的最佳时机。人们会在这一天举行盛大的龙舟竞赛、舞龙、舞狮等传统活动,以示对龙神的崇敬和庆祝丰收的祈愿。同时,二月二也标志着春天的来临,人们用这个节日来祈求来年五谷丰登,农作物顺利生长,以确保社会的安定和民众的生活富裕。



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