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The point of this thread is to find the mathematical error in summing divergent series. For example the series: 1+2+4+8+16+32+64+...+... (doubling the numbers, or alternatively: increasing powers of 2).

I've seen the argument that you multiply the series by 1, then substitute (2-1) for 1. All of the terms cancel except for -1 (the series appears to add to -1).

Now, I tried the same thing but by substituting (3-2) for 1 instead of (2-1), and the series still tends to infinity, which leads me to believe the (-1) of the (2-1) is somehow special.

But also, I noticed that two infinite power series can be multiplied. For example, the series for e^x and the series for sin(x) can be multiplied term wise to give the series for sin(x)e^x.

So my two questions are:

1.) Where is the mathematical fault in the procedure first described? I originally thought you can't multiply a scalar by an infinite series, but it seems that if you can multiply two infinite series you ought to be able to multiply a scalar by an infinite series.

2.) Also, why does substituting (3-2) instead of (2-1) change the result??? Thanks a ton in advance,

Lee

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# Problem with summing a divergent series

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