Chapter 9, Problem 2CT

To determine

To find: An expression for the apparent $n^{th}$ term of the given sequence.

Answer to Problem 2CT

The apparent $n^{th}$ term for the sequence is $a_n=\frac{n+2}{n!}$.

Explanation of Solution

Given:

The given sequence is $\frac{3}{1!},\frac{4}{2!},\frac{5}{3!},\frac{6}{4!},\frac{7}{5!},\dots$.

Calculation:

The values of $n$ are $1,2,3,4,5,\dots$.

The terms are $\frac{3}{1!},\frac{4}{2!},\frac{5}{3!},\frac{6}{4!},\frac{7}{5!},\dots$.

The apparent pattern observed is that for each $n$ , the term in the numerator is $n+2$ and that in the denominator is $n!$.

So, the apparent $n^{th}$ term for the sequence is $a_n=\frac{n+2}{n!}$.