Calculus Examples

$\sum_{i = 1}^{14} - 28 + 3 n$

Step 1

Split the summation into smaller summations that fit the summation rules.

$\sum_{k = 1}^{14} - 28 + 3 n = \sum_{k = 1}^{14} - 28 + 3 \sum_{k = 1}^{14} n$

Step 2

Evaluate $\sum_{k = 1}^{14} - 28$ .

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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.

$(- 28) (14)$

Step 2.3

Multiply $- 28$ by $14$ .

$- 392$

Step 3

Evaluate $3 \sum_{k = 1}^{14} n$ .

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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 and make sure to multiply by the front term.

$(3) ((n) (14))$

Step 3.3

Simplify.

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Step 3.3.1

Move $14$ to the left of $n$ .

$3 (14 n)$

Step 3.3.2

Multiply $14$ by $3$ .

$42 n$

Step 4

Add the results of the summations.

$- 392 + 42 n$