- #1

- 85

- 1

- Thread starter Savant13
- Start date

- #1

- 85

- 1

- #2

- 27

- 3

That series diverges. You got something wrong. Or maybe I don't understand what you are asking.

- #3

lurflurf

Homework Helper

- 2,432

- 132

It depends what you mean by diverges.That series diverges. You got something wrong. Or maybe I don't understand what you are asking.

- #4

- 1,030

- 4

The arithmetic average of all limit points.

- #5

daniel_i_l

Gold Member

- 867

- 0

Maybe you mean the series (1,-1,1,-1,...). In that case Euler used the formula for the power series (that (1,x,x^2...) converges to 1/(1-x)) where x=-1. Then he got 1/(1-(-1)) = 1/2. But with the modern definition of convergence, the formula is only true when -1<x<1.

- #6

- 256

- 0

I believe the technique you're looking for is called Cesaro Summation...check it out on Wikipedia.

- #7

- 85

- 1

Yes, Cesaro summation. That's what I was looking for.

- #8

- 534

- 1

That's a sequence, not a series.

- #9

- 256

- 0

- #10

- 534

- 1

Series are usually written as summations though.

- #11

- 256

- 0

- #12

- 85

- 1

Same thingThat's a sequence, not a series.

- #13

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 956

- #14

- 85

- 1

The example I gave was a harmonic series

- #15

- 119

- 0

No, it was a sequence.

You have a bunch of numbers, a series is a bunch of numbers with an operator.

You have a bunch of numbers, a series is a bunch of numbers with an operator.

- #16

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 956

- #17

- 655

- 3

Dude, this is trivial nomenclature. It's obvious he knows what he means, and it's obvious everyone else knew what he meant, and were able to answer his question. In math it is not the name that is important but rather the meaning and structure.

- #18

lurflurf

Homework Helper

- 2,432

- 132

That is true we do use mophisms, but in the communication of math name is very important. If you do not communicate clearly the meaning and structure of the objects you describe will be changed.In math it is not the name that is important but rather the meaning and structure.

What is the sum of [sin(x)]^2 by [cos(x)]^2?

[tanh(x)]^2

- Last Post

- Replies
- 4

- Views
- 3K

- Last Post

- Replies
- 3

- Views
- 1K

- Last Post

- Replies
- 13

- Views
- 6K

- Last Post

- Replies
- 1

- Views
- 594

- Replies
- 3

- Views
- 9K

- Replies
- 14

- Views
- 1K

- Last Post

- Replies
- 9

- Views
- 3K

- Last Post

- Replies
- 2

- Views
- 1K

- Last Post

- Replies
- 23

- Views
- 1K

- Last Post

- Replies
- 25

- Views
- 4K