Questions: Rewrite the series using summation notation. Use 1 as the lower limit of summation. 8 + 8^2 / 2 + 8^3 / 3 + ... + 8^n / n (Type an expression using i as the variable.)

Solution Steps

To rewrite the given series using summation notation, we need to identify the general term of the series. The given series is: \[ 8 + \frac{8^2}{2} + \frac{8^3}{3} + \cdots + \frac{8^n}{n} \]

The general term of the series can be written as: \[ \frac{8^i}{i} \]

where \( i \) ranges from 1 to \( n \). Therefore, the series can be expressed in summation notation as: \[ \sum_{i=1}^{n} \frac{8^i}{i} \]

The given series is: \[ 8 + \frac{8^2}{2} + \frac{8^3}{3} + \cdots + \frac{8^n}{n} \] We can identify the general term of the series as: \[ \frac{8^i}{i} \] where \( i \) is the index of summation.

Using the general term identified, we can express the entire series in summation notation: \[ \sum_{i=1}^{n} \frac{8^i}{i} \]

Final Answer