Precalculus Examples

$\sum_{m = 11}^{99} 4$

Step 1

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

$\sum_{m = 11}^{99} 4 = \sum_{m = 1}^{99} 4 - \sum_{m = 1}^{10} 4$

Step 2

Evaluate $\sum_{m = 1}^{99} 4$ .

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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.

$(4) (99)$

Step 2.3

Multiply $4$ by $99$ .

$396$

Step 3

Evaluate $\sum_{m = 1}^{10} 4$ .

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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.

$(4) (10)$

Step 3.3

Multiply $4$ by $10$ .

$40$

Step 4

Replace the summations with the values found.

$396 - 40$

Step 5

Subtract $40$ from $396$ .

$356$