Q. 35 - Calculus

Question

In Exercises 31–36 provide the first five terms of the given sequence. Unless specified, assume that the first term has index 1. 

$\left\{\frac{\sqrt{k}}{k}\right\}$

Step-by-Step Solution

Answer

The first five terms of the sequence are $1,\frac{1}{\sqrt{2}},\frac{1}{\sqrt{3}},\frac{1}{2},\frac{1}{\sqrt{5}}.$

Step 1. Given information.

The given sequence is $\left\{\frac{\sqrt{k}}{k}\right\}$.

Step 2. First term.

The general sequence is $a_k=\frac{\sqrt{k}}{k}$.

For the first term, $k=1,$

$a_1=\frac{\sqrt{1}}{1}=1$

Step 3. Remaining Terms.

Now, put

$$\begin{gathered} k=2, \\ {a}_2=\frac{\sqrt{2}}{2} \\ {a}_2=\frac{1}{\sqrt{2}} \\ k=3, \\ {a}_3=\frac{\sqrt{3}}{3} \\ {a}_3=\frac{1}{\sqrt{3}} \\ k=4, \\ {a}_4=\frac{\sqrt{4}}{4}=\frac{1}{2} \\ k=5, \\ {a}_5=\frac{\sqrt{5}}{5} \\ {a}_5=\frac{1}{\sqrt{5}} \end{gathered}$$