S-s=1? S=1-1+1-1..., -S will be -S=-1+1-1+1...

[Hectza]

My very first post here!

I’ve always had this question:

For a series S with the form S=1-1+1-1..., -S will be -S=-1+1-1+1...
Therefore, S-S=1+(-1+1-1+1-1...)-(-1+1-1+1-1...); S-S=1?

I know there’s something going on there that I just can’t see. Is it the perception of the infinite series? Is maths broken? Thanks in advance

 

[mmm4444bot]

For a series S with the form S=1-1+1-1..., -S will be -S=-1+1-1+1...
Therefore, S-S=1+(-1+1-1+1-1...)-(-1+1-1+1-1...); S-S=1?

I know there’s something going on there that I just can’t see.

Perhaps, you're not combining an equal number of terms. Your typing subtracts only five (blue) terms from the six (red) terms listed. Did you then assume that all remaining terms cancel out one another? They don't. :cool:

To see what's up, arrange S and -S vertically, and then add:

[FONT=courier new]
     S =   1   + (-1)  +   1   + (-1)  +   1   + (-1) + …
+   -S = (-1)  +   1   + (-1)  +   1   + (-1)  +   1  + …
  -------------------------------------------------------
     0 =   0   +   0   +   0   +   0   +   0   +   0  + …
[/FONT]

 

[tkhunny]

Maths is not broken.
Try infinite addition only on CONVERGING series.
Please study LOTS about Convergence before playing with infinite series.
Keep your eye on the different kinds of convergence, particularly "Uniform".