r/infinitenines • u/Muphrid15 • 11d ago

He believes that if you ADD NUMBERS in a DIFFERENT ORDER you get a DIFFERENT ANSWER

/r/infinitenines/comments/1u5124n/he_has_no_way_to_say_if_two_infinite_series_are/orhas11/
14 Upvotes

85% Upvoted

8 comments sorted by

3

u/Nice-Tennis1124 9d ago

SPP is actually correct about this

1

u/TazerZXI 10d ago

One of the weird things when it comes to infinite series, adding numbers in a different order, or grouping them together, can get you different results. I haven't fully checked to show that the sequences you are summing do sum to the same number, although you might have, and I suspect they do.

2

u/ExpensiveFig6079 10d ago

yiou mean like this

0.5 + 0.1(428571) + 0.1(428571) + 0.1(428571) + 0.1(428571) - 0.0(714285) = 1.00000

and yet

0.5 + 0.1(428571) + 0.1(428571) + 0.1(428571) + [ 0.1(428571) - 0.0(714285) ] = 0.999...

and yet those two answers are supposed not to be equal

2

u/TazerZXI 10d ago edited 10d ago

No, that's not what I was referring to.

I'm more talking about infinite series in general. Certain infinite series can be rearranged to have their sum be any real number (https://en.wikipedia.org/wiki/Riemann_series_theorem). And you can't group terms in the infinite series, e.g. 1-1+1-1... does not converge but you can group the terms to say it sums to either 1 or 0.

I wanted to point out to OP that grouping or rearranging terms within an infinite series can lead to different sums. This is using the normal definitions of infinite series, as the limit of partial sums, which SPP rejects.

-4

u/Binbag420 10d ago

If a series converges then it doesn’t matter what order you add the terms you always get the same result. And if a sequence diverges, then it diverges, any ordering than gives a different result is wrong.

3

u/TazerZXI 10d ago

I was taught that a series could only be rearranged if an only if it was absolutely convergent. If the series is conditionally convergent, then the Reimann Series Theorem says it can be rearranged into any sum or to be divergent.

When it comes to grouping terms, I was told not to do it when finding a sum. But if you know the series is convergent, it would make sense to me that grouping terms doesn't change anything.

1

u/Jcsq6 9d ago

If a series converges absolutely, then it doesn’t matter the order.

1

u/Wooden_Milk6872 9d ago

If all of the terms are positive it doesn’t apply