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?
$\sum\limits_{i=1}\square$

Explanation:

Step1: Analyze the terms

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

Step2: Determine the upper limit

Since the last term has \(n\) in the denominator and exponent, the upper limit of summation should be \(n\) because when \(i = n\), the term is \(\frac{2^{n}}{n}\) which matches the last term of the given sum.

Answer:

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