Question

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

$\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+.....+\frac{13}{13+1}$

Short answer

The required summation notation is $\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+.....+\frac{13}{13+1}=\sum _{k=1}^{13}\frac{k}{k+1}$.

Step-by-step solution

Step 1. Write the given information.

The given sum is:

$\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+.....+\frac{13}{13+1}$

Step 2. Write the sum using summation notation.

As we can see that the sum $\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+.....+\frac{13}{13+1}$has 13 terms, each term represents the form $\frac{k}{k+1}$, and this sum starts at $\frac{1}{2}$and ends at $\frac{13}{13+1}$.

Therefore,$\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+.....+\frac{13}{13+1}=\sum _{k=1}^{13}\frac{k}{k+1}$.