Chapter 12.1, Problem 67AYU

In Problems 61-70, express each sum using summation notation.

$3+\frac{3^2}{2}+\frac{3^3}{3}+\mathrm{...}+\frac{3^n}{n}$

To determine

To find: The sum using summation notation: $3+\frac{3^2}{2}+\frac{3^3}{3}+\dots \dots \mathrm{..}+\frac{3^n}{n}$.

Answer to Problem 67AYU

$3+\frac{3^2}{2}+\frac{3^3}{3}+\dots \dots \mathrm{..}+\frac{3^n}{n}={\displaystyle \sum }_{k=1}^n\frac{3^K}{K}$

Explanation of Solution

Given:

$3+\frac{3^2}{2}+\frac{3^3}{3}+\dots \dots \mathrm{..}+\frac{3^n}{n}$

Calculation:

$3+\frac{3^2}{2}+\frac{3^3}{3}+\dots \dots \mathrm{..}+\frac{3^n}{n}={\displaystyle \sum }_{k=1}^n\frac{3^K}{K}$