QuestionExpress the sum using summation notation. Use 1 as the lower limit of summation and ifor the index of summation. $\begin{array}{c} 8+8^{2}+8^{3}+\cdots+8^{10} \\ 8+8^{2}+8^{3}+\cdots+8^{10}=\sum \square \end{array}$

Studdy Solution

STEP 1

1. The problem requires expressing a series using summation notation.
2. The series is a geometric series with a common base of 8.
3. The series starts at $8^1$ and ends at $8^{10}$ .

STEP 2

1. Identify the pattern in the series.
2. Express the series using summation notation.

STEP 3

Identify the pattern in the series. The given series is:
$8 + 8^2 + 8^3 + \cdots + 8^{10}$
This is a geometric series where each term is $8^i$ , starting from $i=1$ to $i=10$ .

STEP 4

Express the series using summation notation. The series can be written as:
$\sum_{i=1}^{10} 8^i$
This notation indicates that the sum of $8^i$ is taken from $i=1$ to $i=10$ .
The sum using summation notation is:
$\sum_{i=1}^{10} 8^i$

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