Problem 40 - College Algebra

Question

Find each indicated sum. $$\sum_{i=0}^{4} \frac{(-1)^{i+1}}{(i+1) !}$$

Step-by-Step Solution

Answer

The sum of the series is \(-\frac{47}{120}\).

Step 1: Understand the Summation Expression

In the expression, \(\sum_{i=0}^{4} \frac{(-1)^{i+1}}{(i+1) !}\), the \(i\) is the variable that controls the summation starting from 0 to 4. For each value of \(i\), compute \(\frac{(-1)^{i+1}}{(i+1) !}\).

Step 2: Substituting values

For each value of \(i\) from 0 to 4, substitute the values into the expression. This gives \[(-1)+\frac{1}{2}-\frac{1}{6}+\frac{1}{24}-\frac{1}{120}\].

Step 3: Perform the Calculations

Add up all the values calculated in the previous step to find the sum of the series. \[(-1)+\frac{1}{2}-\frac{1}{6}+\frac{1}{24}-\frac{1}{120}=-\frac{47}{120}\]