Question

Find the least upper bound of the sequences in Exercises 37–42

$\left\{2-\frac{1}{k^2}\right\}$

Short answer

The east upper bound is$2.$

Step-by-step solution

Step 1. Given information.

The given series is$\left\{2-\frac{1}{k^2}\right\}$.

Step 2. Upper bound.

Now, we can write,

$$\begin{gathered} \underset{k\to \infty }{\lim }{a}_k=\underset{k\to \infty }{\lim }\left(2-\frac{1}{k^2}\right) \\ =\underset{k\to \infty }{\lim }2-\underset{k\to \infty }{\lim }\left(\frac{1}{k^2}\right) \\ =2 \end{gathered}$$