Which of the following represents $\sum_{n=1}^{104} 6$?
A. $(1 \times 6)+(104 \times 6)=630$
B. $(1 \times 6) \times(104 \times 6)=3,744$
C. $6(104)=624$
D. $6(104-1)=618$
Answer (2)
The problem requires to find the expression that represents the sum of a constant value (6) from n=1 to n=104.
Recognize that the summation ∑ n = 1 104 6 means adding the number 6 to itself 104 times, which is equivalent to multiplying 6 by 104.
Calculate the product: 6 × 104 = 624 .
The correct representation of the summation is 6 ( 104 ) = 624 .
Explanation
Understanding the Problem We are asked to find the expression that represents the sum of a constant value (6) from n=1 to n=104. This means we need to add the number 6 to itself 104 times.
Expressing the Summation as Multiplication The summation ∑ n = 1 104 6 is equivalent to multiplying 6 by 104.
Calculating the Product We calculate the product of 6 and 104: 6 × 104 = 624 .
Identifying the Correct Option Now, we compare the result with the given options to find the correct one. The option that matches our result is 6 ( 104 ) = 624 .
Final Answer Therefore, the correct representation of the summation is 6 ( 104 ) .
Examples
Imagine you're saving money, and every day for 104 days, you save 6. T h es u mma t i o n \sum_{n=1}^{104} 6$ represents the total amount of money you've saved over those 104 days. This is a simple example of how repeated addition, represented by a summation, can be used to calculate cumulative savings or earnings over a period of time. Understanding summations helps in various financial calculations, such as calculating total interest earned or total expenses over a specific period.
The summation ∑ n = 1 104 6 represents adding the number 6 a total of 104 times, which is equivalent to 6 × 104 = 624 . The correct option from the choices given is C : 6 ( 104 ) = 624 .
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