Calculus Examples

$\sum_{k = 5}^{26} 4$

Step 1

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

$\sum_{k = 5}^{26} 4 = \sum_{k = 1}^{26} 4 - \sum_{k = 1}^{4} 4$

Step 2

Evaluate $\sum_{k = 1}^{26} 4$ .

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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.

$(4) (26)$

Step 2.3

Multiply $4$ by $26$ .

$104$

Step 3

Evaluate $\sum_{k = 1}^{4} 4$ .

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Step 3.1

Expand the series for each value of $k$ .

$4 + 4 + 4 + 4$

Step 3.2

Simplify.

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Step 3.2.1

Add $4$ and $4$ .

$8 + 4 + 4$

Step 3.2.2

Add $8$ and $4$ .

$12 + 4$

Step 3.2.3

Add $12$ and $4$ .

$16$

Step 4

Replace the summations with the values found.

$104 - 16$

Step 5

Subtract $16$ from $104$ .

$88$