Let's say for example these two:3n2n+3(−1)n+1−(−1)n2n((−1)n+1n)2

"Let's say for example these two:3n2n+3(−1)n+1−(−1)n2n((−1)n+1n)2" was answered by our experts

basura8w081

2022-03-23

Let's say for example these two:

\frac{3 n}{2 n + 3} {(- 1)}^{n + 1} - \frac{{(- 1)}^{n}}{2 n} {({(- 1)}^{n} + \frac{1}{n})}^{2}

Alannah Campos

Beginner2022-03-24Added 10 answers

If you just want the bounded property, you can simply find crude upper and lower bounds.
E.g. if

{(- 1)}^{n} + \frac{1}{n}

is bounded, then so is

{({(- 1)}^{n} + \frac{1}{n})}^{2}

(so we can essentially disregard the power of 2). Then we note that both

{(- 1)}^{n}

and

\frac{1}{n}

are between

- 1

and 1 for all

n \geq 1

(I told you it was crude). Hence

- 2 \leq {(- 1)}^{n} + \frac{1}{n} \leq 2

and

{({(- 1)}^{n} + \frac{1}{n})}^{2} \leq 4

The first sequence

\frac{3 n}{2 n + 3} {(- 1)}^{n + 1} - \frac{{(- 1)}^{n}}{2 n}

can be resolved by similar techniques.

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