([13],[0])+([13],[1])+([13],[2])+([13],[3])+([13],[4])+([13],[5])+([13],[6])

Understand the problem: Understand the problem. We are given a series of tuples to add together. Each tuple consists of two elements, where the first element is the number 13 and the second element is a number ranging from 0 to 6. To add tuples, we add the corresponding elements of each tuple together.Add first elements: Add the first elements of each tuple. Since the first element of each tuple is 13, we will add 13 to itself seven times (because there are seven tuples). 13 + 13 + 13 + 13 + 13 + 13 + 13 This is equivalent to multiplying 13 by 7. 13 * 7 = 91Add second elements: Add the second elements of each tuple. The second elements of the tuples are the numbers from 0 to 6. We will add these numbers together. 0 + 1 + 2 + 3 + 4 + 5 + 6 This is a sum of an arithmetic series with the first term a_1 = 0, the last term a_n = 6, and the number of terms n = 7. The sum of this series is given by the formula: S_n = n/2 * (a_1 + a_n) S_7 = 7/2 * (0 + 6) = 7/2 * 6 = 21Combine sums: Combine the sums to form the final tuple. The sum of the first elements is 91, and the sum of the second elements is 21. We combine these sums to form the final tuple. Final tuple = (91, 21)

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([13],[0])+([13],[1])+([13],[2])+([13],[3])+([13],[4])+([13],[5])+([13],[6])

$\left(\begin{array}{c}13 \\ 0\end{array}\right)+\left(\begin{array}{c}13 \\ 1\end{array}\right)+\left(\begin{array}{c}13 \\ 2\end{array}\right)+\left(\begin{array}{c}13 \\ 3\end{array}\right)+\left(\begin{array}{c}13 \\ 4\end{array}\right)+\left(\begin{array}{c}13 \\ 5\end{array}\right)+\left(\begin{array}{c}13 \\ 6\end{array}\right)$

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Math Problems

Algebra 1

Multiplication with rational exponents

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\left(\begin{array}{c}13 \\ 0\end{array}\right)+\left(\begin{array}{c}13 \\ 1\end{array}\right)+\left(\begin{array}{c}13 \\ 2\end{array}\right)+\left(\begin{array}{c}13 \\ 3\end{array}\right)+\left(\begin{array}{c}13 \\ 4\end{array}\right)+\left(\begin{array}{c}13 \\ 5\end{array}\right)+\left(\begin{array}{c}13 \\ 6\end{array}\right)

Understand the problem: Understand the problem. $\newline$ We are given a series of tuples to add together. Each tuple consists of two elements, where the first element is the number $13$ and the second element is a number ranging from $0$ to $6$ . To add tuples, we add the corresponding elements of each tuple together.
Add first elements: Add the first elements of each tuple. $\newline$ Since the first element of each tuple is $13$ , we will add $13$ to itself seven times (because there are seven tuples). $\newline$ $13 + 13 + 13 + 13 + 13 + 13 + 13$ $\newline$ This is equivalent to multiplying $13$ by $7$ . $\newline$ $13 \times 7 = 91$
Add second elements: Add the second elements of each tuple. $\newline$ The second elements of the tuples are the numbers from $0$ to $6$ . We will add these numbers together. $\newline$ $0 + 1 + 2 + 3 + 4 + 5 + 6$ $\newline$ This is a sum of an arithmetic series with the first term $a_1 = 0$ , the last term $a_n = 6$ , and the number of terms $n = 7$ . $\newline$ The sum of this series is given by the formula: $S_n = \frac{n}{2} * (a_1 + a_n)$ $\newline$ $S_7 = \frac{7}{2} * (0 + 6) = \frac{7}{2} * 6 = 21$
Combine sums: Combine the sums to form the final tuple. $\newline$ The sum of the first elements is $91$ , and the sum of the second elements is $21$ . We combine these sums to form the final tuple. $\newline$ Final tuple = $(91, 21)$