- #1

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- 2

## Homework Statement

Find whether the following converge or diverge

A:[itex]\sum_{n=1}^{\infty} \frac{n-1}{n}[/itex]

B:[itex]\sum_{n=1}^{\infty} \frac{1}{n^{\frac{3}{2}}}[/itex]

## Homework Equations

## The Attempt at a Solution

Again really not sure how to show this mathematically, not even sure if what I have done is correct so any help or advice is much appreciated.

A:

[tex]

\sum_{n=1}^{\infty} \frac{n-1}{n}=\frac{\frac{n}{n}-\frac{1}{n}}{\frac{n}{n}}=1-\frac{1}{n} \\

=1-1+1-\frac{1}{2}+1-\frac{1}{3}+1-\frac{1}{4}...[/tex]

here it seems it diverges to infinity as n tends to infinity (due to the +1's)

B:

[tex]

\sum_{n=1}^{\infty} \frac{1}{n^{\frac{3}{2}}}=1+0.353+0.192+...[/tex]

Here is looks like it converges to the limit of 2 as n tends to infinity.