是不是有纹身就不能考教师资格证？？-专业的问答平台
来自：本站 添加时间：2025-05-25 02:43
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. 车身尺寸方面，探界者EV长宽高分别为4845mm*1913mm*1644mm，轴距为2945mm，比燃油版探界者更长、更宽，轴距也更大，在奥特能平台之下，预计它的空间表现不错。
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