- #1

- 40

- 0

## Homework Statement

First, I'd like to thank everybody a head of time. You guys have been an enormous help.

Second, I don't mind telling you that I'm finding sequences and series extremely frustrating. I usually pick this stuff up like nobody's business.

My problem is attached, but I will copy it down as I understand it.

[itex]

r = \frac{11}{24}

[/itex]

[itex]

\sum _{i=1} ^\inf nr^n

[/itex]

Mysteriously, this can be rewritten as

[itex]

\sum_{i=1} ^n ir^i = \frac{ nr^{n+2} - (n+1)r^{n+1} + r }{ (1 - r)^2 }

[/itex]

## Homework Equations

[itex]

\sum _{i=1} ^\inf nr^n \rightarrow

n \sum _{i=1} ^\inf r^n \rightarrow

n \frac{1}{1-r}

[/itex]

## The Attempt at a Solution

[itex]

\sum _{i=1} ^\inf nr^n \rightarrow

n \sum _{i=1} ^\inf r^n \rightarrow

n \frac{1}{1-r}

[/itex]

[itex]

\frac{1}{1-r}

[/itex]

This is a number greater than one,

[itex]

\frac{24}{13}

[/itex]

So as n goes to infinity, the number just gets bigger and bigger right? Diverges to infinite is, apparently, not the answer.