Problem 41 - College Algebra

Question

Find each indicated sum. $$\sum_{i=1}^{5} \frac{i !}{(i-1) !}$$

Step-by-Step Solution

Answer

The sum of the series is 15.

Step 1: Understanding the problem

The series given is \(\sum_{i=1}^{5} \frac{i !}{(i-1) !}\). The aim is to find the sum of this series. By applying the property of factorials \(n ! = n \cdot (n - 1) !\), the fraction \(\frac{i !}{(i-1) !}\) simplifies to \(i\).

Step 2: Applying the factorial property

We substitute \(\frac{i !}{(i-1) !}\) to \(i\). This simplifies the series to \(\sum_{i=1}^{5} i\).

Step 3: Calculating the sum of the series

Now, the aim is to find the sum of first 5 natural numbers, which comes out to be 1 + 2 + 3 + 4 + 5 = 15.