Infinitely maddening

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When you grow up, do you expect to be like Gauss in mathematics?

Yes I do.

So is your self-reference as 'Baby Gauss' based only upon 'kicking the butts' of 'above average' undergraduate students at your local university?

Yes it is.

😏😏😏

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1 + 1/2 + 1/4 + 1/8 + ... = 1

How about 1 + 1/2 + 1/4 + 1/8 + ... = 2 ?

The post that was quoted here has been removed

Almost certainly, yes.

Originally posted by FabianFnas
1 + 1/2 + 1/4 + 1/8 + ... = 1

How about 1 + 1/2 + 1/4 + 1/8 + ... = 2 ?

Yes, in the thread we were actually discussing both the series 1/2 + 1/4 + 1/8 + ··· and 1 + 1/2 + 1/4 + ···, so it was a fairly natural mistake to make.

Originally posted by DeepThought
Yes, in the thread we were actually discussing both the series 1/2 + 1/4 + 1/8 + ··· and 1 + 1/2 + 1/4 + ···, so it was a fairly natural mistake to make.

So now everyone agree that 1/2 + 1/4 + 1/8 + ... exactly = 1 finally...?

Originally posted by FabianFnas
So now everyone agree that 1/2 + 1/4 + 1/8 + ... exactly = 1 finally...?

Yes, although if we wait for a year or two I bet this comes up again...

Originally posted by DeepThought
Yes, in the thread we were actually discussing both the series 1/2 + 1/4 + 1/8 + ··· and 1 + 1/2 + 1/4 + ···, so it was a fairly natural mistake to make.

Natural, but careless of my part.

Originally posted by FabianFnas
So now everyone agree that 1/2 + 1/4 + 1/8 + ... exactly = 1 finally...?

Only on condition that the '=' does not mean quite the same as it does in normal equations. In this case the '=' is defined slightly differently.

Originally posted by twhitehead
Only on condition that the '=' does not mean quite the same as it does in normal equations. In this case the '=' is defined slightly differently.

It is seldom clear when you are being serious and when you are not.

Originally posted by Soothfast
It is seldom clear when you are being serious and when you are not.

I am being serious. In this instance the final 'sum' of the sequence is defined as being the limit of the partial sums of the sequence. It is not the case that an infinite number of terms are actually added to give exactly 1.

Originally posted by twhitehead
I am being serious. In this instance the final 'sum' of the sequence is defined as being the limit of the partial sums of the sequence. It is not the case that an infinite number of terms are actually added to give exactly 1.

If the sum (call it S) is not equal to 1.
Then what is (1 - S) ?

Originally posted by wolfgang59
If the sum (call it S) is not equal to 1.
Then what is (1 - S) ?

I do not believe the sum can be obtained. It is incoherent to talk of the sum of an infinite sequence without specifically redefining what we mean by 'sum'.
The problems associated with summing an infinite number of terms is especially noticeable when dealing with series that do not converge.