sum_(n=1)^(3)(n^(2)-1)=

Understanding the series: Understand the series and the formula to be used. We need to calculate the sum of the series for the expression (n^2 - 1) where n ranges from 1 to 3.Calculating the first term: Calculate the first term of the series when n=1. Substitute n=1 into the expression (n^2 - 1). (1^2 - 1) = (1 - 1) = 0Calculating the second term: Calculate the second term of the series when n=2. Substitute n=2 into the expression (n^2 - 1). (2^2 - 1) = (4 - 1) = 3Calculating the third term: Calculate the third term of the series when n=3. Substitute n=3 into the expression (n^2 - 1). (3^2 - 1) = (9 - 1) = 8Summing the values: Sum the values obtained for n=1, n=2, and n=3. Sum = 0 + 3 + 8 Sum = 11

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Math Problems

Algebra 2

Composition of linear and quadratic functions: find a value

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\sum_{n=1}^{3}\left(n^{2}-1\right)=

Understanding the series: Understand the series and the formula to be used. $\newline$ We need to calculate the sum of the series for the expression $n^2 - 1$ where $n$ ranges from $1$ to $3$ .
Calculating the first term: Calculate the first term of the series when $n=1$ . Substitute $n=1$ into the expression $(n^2 - 1)$ . $(1^2 - 1) = (1 - 1) = 0$
Calculating the second term: Calculate the second term of the series when $n=2$ . $\newline$ Substitute $n=2$ into the expression $(n^2 - 1)$ . $\newline$ $(2^2 - 1) = (4 - 1) = 3$
Calculating the third term: Calculate the third term of the series when $n=3$ . Substitute $n=3$ into the expression $(n^2 - 1)$ . $(3^2 - 1) = (9 - 1) = 8$
Summing the values: Sum the values obtained for $n=1$ , $n=2$ , and $n=3$ . $\text{Sum} = 0 + 3 + 8$ $\text{Sum} = 11$