Chapter 9.1, Problem 1E

To determine

To Compute: The first $4$ terms and the ${50}^{th}$ term of a given sequence with specified $n^{th}$ term.

Answer to Problem 1E

The first four terms and the fiftieth term of the sequence are $\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5}$ and $\frac{50}{51}$ respectively

Explanation of Solution

Given Information: The $n^{th}$ term of the sequence is given by $a_n=\frac{n}{n+1}$

Method: Substitute the values $n=1,2,3,4$ and $50$ in the expression for the $n^{th}$ term and evaluate it.

Calculation:

  $a_1=\frac{1}{1+1}=\frac{1}{2}$

  $a_2=\frac{2}{2+1}=\frac{2}{3}$

  $a_3=\frac{3}{3+1}=\frac{3}{4}$

  $a_4=\frac{4}{4+1}=\frac{4}{5}$

  $⋮$

  $a_{50}=\frac{50}{50+1}=\frac{50}{51}$

Therefore, the first four terms and the ${50}^{th}$ term are $\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5}$ and $\frac{50}{50+1}$ respectively.