Precalculus Examples

$\sum_{0}^{20} 3 {(\frac{3}{2})}^{0}$

Step 1

Simplify the summation.

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Step 1.1

Apply the product rule to $\frac{3}{2}$ .

$3 \frac{3^{0}}{2^{0}}$

Step 1.2

Anything raised to $0$ is $1$ .

$3 \frac{1}{2^{0}}$

Step 1.3

Anything raised to $0$ is $1$ .

$3 (\frac{1}{1})$

Step 1.4

Cancel the common factor of $1$ .

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Step 1.4.1

Cancel the common factor.

$3 (\frac{1}{1})$

Step 1.4.2

Rewrite the expression.

$3 \cdot 1$

Step 1.5

Multiply $3$ by $1$ .

$3$

Step 1.6

Rewrite the summation.

$\sum_{i = 0}^{20} 3$

Step 2

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

$\sum_{i = 0}^{20} 3 = \sum_{i = 1}^{20} 3 + \sum_{i = 0}^{0} 3$

Step 3

Evaluate $\sum_{i = 1}^{20} 3$ .

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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.

$(3) (20)$

Step 3.3

Multiply $3$ by $20$ .

$60$

Step 4

Expand the series for each value of $i$ .

$3$

Step 5

Replace the summations with the values found.

$60 + 3$

Step 6

Add $60$ and $3$ .

$63$