发现与分享，畅游显卡更新驱动以后不显示了怎么办的乐趣
来自：本站 添加时间：2025-05-24 19:52
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. 一方面要多渠道增加能源供应，积极协调落实电、煤和天然气合同签约履约情况，做好应急资源储备和保供稳价，及时落实相关资金补贴政策，保障供暖平稳有序、高质高效。 近年来，北川妇联用“宽度”“广度”“温度”，全面落实妇女儿童维权“五项机制”，着力构建妇女儿童维权工作新格局。
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