Question

express the sum using summation notation. use 1 as the lower limit of summation and i for the index of summation.
$2 + \frac{2^2}{2} + \frac{2^3}{3} + \dots + \frac{2^n}{n}$
the summation starts at i = 1. what is the upper limit of summation and the general term?
$\sum_{i=1}^{\square} \square$

Explanation:

Step1: Analyze the terms

The first term is when \(i = 1\): \(2=\frac{2^{1}}{1}\), the second term when \(i = 2\): \(\frac{2^{2}}{2}\), the third term when \(i=3\): \(\frac{2^{3}}{3}\), and the last term is when \(i = n\): \(\frac{2^{n}}{n}\).

Step2: Determine the general term and upper limit

The general term for the \(i\)-th term is \(\frac{2^{i}}{i}\), and the upper limit of summation is \(n\) since the last term is when \(i = n\).

Answer:

\(\sum_{i = 1}^{n}\frac{2^{i}}{i}\)