Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
To find the sum of the series [tex]\(1 + 2 + 3 + \cdots + 460\)[/tex], you can use the formula for the sum of the first [tex]\(n\)[/tex] natural numbers:
[tex]\[ S = \frac{n(n + 1)}{2} \][/tex]
where [tex]\(n\)[/tex] is the last number in the series.
In this problem, the series goes up to 460, so [tex]\(n = 460\)[/tex]. Plugging this value into the formula, we get:
[tex]\[ S = \frac{460 (460 + 1)}{2} \][/tex]
1. First, calculate [tex]\(460 + 1\)[/tex]:
[tex]\[ 460 + 1 = 461 \][/tex]
2. Next, multiply 460 by 461:
[tex]\[ 460 \times 461 = 211060 \][/tex]
3. Finally, divide the result by 2 to find the sum:
[tex]\[ S = \frac{211060}{2} = 105530 \][/tex]
Thus, the sum of the series [tex]\(1 + 2 + 3 + \cdots + 460\)[/tex] is [tex]\(\boxed{105530}\)[/tex].
[tex]\[ S = \frac{n(n + 1)}{2} \][/tex]
where [tex]\(n\)[/tex] is the last number in the series.
In this problem, the series goes up to 460, so [tex]\(n = 460\)[/tex]. Plugging this value into the formula, we get:
[tex]\[ S = \frac{460 (460 + 1)}{2} \][/tex]
1. First, calculate [tex]\(460 + 1\)[/tex]:
[tex]\[ 460 + 1 = 461 \][/tex]
2. Next, multiply 460 by 461:
[tex]\[ 460 \times 461 = 211060 \][/tex]
3. Finally, divide the result by 2 to find the sum:
[tex]\[ S = \frac{211060}{2} = 105530 \][/tex]
Thus, the sum of the series [tex]\(1 + 2 + 3 + \cdots + 460\)[/tex] is [tex]\(\boxed{105530}\)[/tex].
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.