Calculus Examples

$\sum_{i = 0}^{6} 10 (\frac{2}{5})$

Step 1

Simplify the summation.

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Step 1.1

Cancel the common factor of $5$ .

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Step 1.1.1

Factor $5$ out of $10$ .

$5 (2) \frac{2}{5}$

Step 1.1.2

Cancel the common factor.

$5 \cdot 2 \frac{2}{5}$

Step 1.1.3

Rewrite the expression.

$2 \cdot 2$

Step 1.2

Multiply $2$ by $2$ .

$4$

Step 1.3

Rewrite the summation.

$\sum_{i = 0}^{6} 4$

Step 2

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

$\sum_{i = 0}^{6} 4 = \sum_{i = 1}^{6} 4 + \sum_{i = 0}^{0} 4$

Step 3

Evaluate $\sum_{i = 1}^{6} 4$ .

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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.

$(4) (6)$

Step 3.3

Multiply $4$ by $6$ .

$24$

Step 4

Expand the series for each value of $i$ .

$4$

Step 5

Replace the summations with the values found.

$24 + 4$

Step 6

Add $24$ and $4$ .

$28$