最佳回答
(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.
首先,喝白开水能够提高人体的新陈代谢,加快循环速度并提高代谢能力,有助于排出体内的废物。, “春节后,应该就能吃上新鲜的无菌鸡蛋了。
如何评价陆_知马俐?本剧有什么内涵?
陆知马俐是一部由电视剧《陆小凤传奇之十三凤钗》中的女主角角色,由中国女演员赵雅芝饰演。 陆知马俐是一个勇敢、聪明、机智的女性角色,她具有非常高的智商和极强的领悟能力。她在剧中扮演着陆小凤的好友、帮手和盟友,与陆小凤一起解决复杂的案件和戏剧性的情节。 评价陆知马俐时,可以说她是一个非常坚强和独立的女性,具有强烈的正义感和责任感。她能够处理复杂的情况,并在危难时刻保护自己和身边的人,展现出了极大的勇气和智慧。她的角色也展示了女性的独立性和坚韧性,给观众留下了深刻的印象。 《陆小凤传奇之十三凤钗》这部剧的内涵丰富多彩。首先,故事情节引人入胜,充满着悬疑和传奇色彩,让观众产生了持续的紧张和期待。其次,剧中的人物塑造饱满,每个角色都有自己的个性特点和丰富的人生经历,展现出了不同的价值观和行为方式。此外,剧中还蕴含了一些人生哲理和道德准则,反映了社会的善恶之间的斗争和角力。这些都使得这部剧在娱乐的同时也具有了一定的思考和启示的作用。 总的来说,陆知马俐是一个非常具有魅力和个性的角色,她的出现丰富了《陆小凤传奇之十三凤钗》这部剧的内涵,并通过故事情节、人物塑造和道德思考等方面给观众带来了深刻的触动和反思。
依托总行在支行设立消费金融直营中心的契机,向信贷客户大力宣传数字人民币贷款和支付优势,通过发放数字人民币贷款,持续激活数字人民币钱包、数字人民币消费、数字人民币支付、数字人民币代发等交易,进一步构建起良好的数字人民币应用生态。, 通讯员 陈培 全媒体首席记者 安富斌 摄
猪蹄要卤多久?
本文共有44人参与回答,点击这里发表你的个人建议吧!
最近更新
向一个男性朋友告白几天后跟他说话有种被宠爱的感觉是错觉吗? 他上次恋爱被背叛受伤很重,现在对感情问
汽车和交通时间:2025-05-23阅读:56 3065条回答
热门标签
友情链接
关注我们
扫一扫二维码下载app