Calculus Examples

$\sum_{n = 0}^{8} x^{n}$

Step 1

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

$\sum_{n = 0}^{8} x^{n} = \sum_{n = 1}^{8} x^{n} + \sum_{n = 0}^{0} x^{n}$

Step 2

Evaluate $\sum_{n = 1}^{8} x^{n}$ .

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Step 2.1

Expand the series for each value of $n$ .

$x^{1} + x^{2} + x^{3} + \dots + x^{8}$

Step 2.2

Simplify the expanded form.

$0$

Step 3

Expand the series for each value of $n$ .

$x^{0}$

Step 4

Replace the summations with the values found.

$0 + x^{0}$

Step 5

Simplify.

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Step 5.1

Add $0$ and $x^{0}$ .

$x^{0}$

Step 5.2

Anything raised to $0$ is $1$ .

$1$