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Topic: The objects that Newton played with were called infinite series
but had ZERO to do with infinity. The name infinite series is a misnomer.

Replies: 9   Last Post: Oct 6, 2017 1:37 AM

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 bursejan@gmail.com Posts: 5,511 Registered: 9/25/16
Re: The objects that Newton played with were called infinite series
but had ZERO to do with infinity. The name infinite series is a misnomer.

Posted: Sep 30, 2017 2:36 PM

This can be used for a little variant of proving
the Cauchy product, we also have:

s_n*t_n - s_(n-1)*t_(n-1) =

(s_n - s_(n-1)) * (t_n + t_(n_1))/2 +

(s_n + s_(n-1))/2 * (t_n - t_(n-1)).

Or graphically:

A A B B _
A A B B _
C C X B _
C C C X _
_ _ _ _ _

Am Samstag, 30. September 2017 20:26:37 UTC+2 schrieb burs...@gmail.com:
> To see how the box is built, consider:
>
> A A B _ _
> A A B _ _
> C C D _ _
> _ _ _ _ _
> _ _ _ _ _
>
> Or algebraically:
>
> s_n*t_n - s_(n-1)*t_(n-1) =
>
> (s_n - s_(n-1)) * t_(n_1) +
>
> s_(n-1) * (t_n - t_(n-1)) +
>
> (s_n - s_(n-1))*(t_n - t_(n-1)) +