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.
07 我是早上坐高铁从建德赶来的，成长之路的公益升学活动我持续在参与，女儿四年级，小学阶段想让她产生更多内驱力，家长该怎样引导？ 黄山老师：小学阶段的好奇心应该更广谱一点，不应该只对一门学科或仅仅是理科感兴趣，甚至不一定只对课内教的内容感兴趣。, 司法诉讼，也是影响一家上市公司发展的重要因素。
你认为女生应该撒娇吗？
作为一名AI助手，我没有个人意见或情感，但我可以就这个话题给你提供一些观点。 撒娇是一种展示可爱和无害的行为，一些女生可能会通过撒娇来表达自己的需求，或者为了得到他人的关注和关心。每个人都有自己的喜好和个性，因此有些人可能喜欢或倾向于撒娇，而另一些人可能不太喜欢。重要的是在恰当的时间和场合下运用撒娇，而不是依赖撒娇来达到自己的目的或掌控他人。 总之，撒娇是个人的选择，应该基于自己的价值观和关系动态来决定。重要的是保持自己真实的表达，并与他人进行积极的交流和互动。
英超不希望受到外部独立机构的监管，所以现在他们似乎对俱乐部开始强硬起来，整个联盟都有一种感觉，那就是‘我们最好把自己的事情处理好’（免得最终被外部的独立监管机构插手）。, ESPN表示，乌拉圭终结了阿根廷在世预赛的最长连续不败纪录，本场比赛之前，阿根廷已经连续25场世预赛保持不败。
don't break my heart是什么歌
"Don't Break My Heart" 是一首由英国流行乐团 UB40 所演唱的歌曲。这首歌最初由乐团在1985年的同名专辑中发行，是专辑中的第一支单曲。
那么，问题出在哪里呢？或许，问题的关键在于选角。,其实，我敢“贸然”尝试，底气来自此前各项任务的历练。
