Precalculus Examples

$\sum_{n = 2}^{7} 2$

Step 1

Split the summation to make the starting value of $n$ equal to $1$ .

$\sum_{n = 2}^{7} 2 = \sum_{n = 1}^{7} 2 - \sum_{n = 1}^{1} 2$

Step 2

Evaluate $\sum_{n = 1}^{7} 2$ .

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Step 2.1

The formula for the summation of a constant is:

$\sum_{k = 1}^{n} c = c n$

Step 2.2

Substitute the values into the formula.

$(2) (7)$

Step 2.3

Multiply $2$ by $7$ .

$14$

Step 3

Expand the series for each value of $n$ .

$2$

Step 4

Replace the summations with the values found.

$14 - 2$

Step 5

Subtract $2$ from $14$ .

$12$