Precalculus Examples

$\sum_{k = 7}^{22} 8.1$

Step 1

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

$\sum_{k = 7}^{22} 8.1 = \sum_{k = 1}^{22} 8.1 - \sum_{k = 1}^{6} 8.1$

Step 2

Evaluate $\sum_{k = 1}^{22} 8.1$ .

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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.

$(8.1) (22)$

Step 2.3

Multiply $8.1$ by $22$ .

$178.2$

Step 3

Evaluate $\sum_{k = 1}^{6} 8.1$ .

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Step 3.1

The formula for the summation of a constant is:

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

Step 3.2

Substitute the values into the formula.

$(8.1) (6)$

Step 3.3

Multiply $8.1$ by $6$ .

$48.6$

Step 4

Replace the summations with the values found.

$178.2 - 48.6$

Step 5

Subtract $48.6$ from $178.2$ .

$129.6$