- #1

- 8

- 0

## Homework Statement

Let x_1=1 and let x_n=x_n-1 + 1/n^n for n>1. Show that x1, x2, ... is convergent.

## Homework Equations

## The Attempt at a Solution

I have managed to transform x_n=summation(1/n^n). How do I show that this is convergent?

- Thread starter economist1985
- Start date

- #1

- 8

- 0

Let x_1=1 and let x_n=x_n-1 + 1/n^n for n>1. Show that x1, x2, ... is convergent.

I have managed to transform x_n=summation(1/n^n). How do I show that this is convergent?

- #2

Office_Shredder

Staff Emeritus

Science Advisor

Gold Member

- 3,904

- 177

You could compare that series with [tex] \sum \frac{1}{n^2}[/tex]

- Last Post

- Replies
- 5

- Views
- 9K

- Last Post

- Replies
- 5

- Views
- 2K

- Last Post

- Replies
- 2

- Views
- 5K

- Last Post

- Replies
- 3

- Views
- 326

- Last Post

- Replies
- 13

- Views
- 2K

- Replies
- 6

- Views
- 1K

- Replies
- 3

- Views
- 3K

- Last Post

- Replies
- 4

- Views
- 446

- Replies
- 5

- Views
- 738

- Replies
- 4

- Views
- 1K