探索知识星球平台，加入是不是南北回归线之间，南北回归线上共享学习乐趣！

探索知识星球平台，加入是不是南北回归线之间，南北回归线上共享学习乐趣！

家里穷，手机买不起怎么办？想买一个手机，64G内存的。

”，重点清理和规范党的十八大以后发生或延续的、影响领导干部公正执行公务的借贷行为，主要有：以本人、亲属或他人名义，利用职权或职务上的影响，以借为名，长期不还，实为利益输送的行为；

(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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朋友间，靠利益能维持多久？

朋友之间靠利益维持的持久性是有限的。尽管利益可以促使人们建立联系和保持友好关系，但当利益消失或发生变化时，友谊可能会受到威胁。真正的友谊应该建立在共同的价值观、互相的尊重和支持的基础上，而不仅仅是利益的交换。这样的友谊更加稳固和持久，不会仅仅受到利益的驱使。

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