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Penulis Topik: DIVISION BY 0  (Dibaca 1382 kali)

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Offline trfrm

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DIVISION BY 0
« pada: Juli 19, 2018, 06:26:48 PM »
Namo amitabha.

In real algebra, the null (0) can be reached from left and from right ... .

In complex algebra, the null (0) can be reached from all directions ... .

Arigatou ikimono gakari.



Tercatat
\[ \sum_{j=0}^\infty \frac{1}{j!(n-j)!} = \frac{2^n}{n!} \]

Offline trfrm

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Re:DIVISION BY 0
« Jawab #1 pada: Juli 19, 2018, 06:28:53 PM »
Namo Buddhaya.

$(1 - 1 + 1 - 1 + \cdots)$ is not 0 ... because we don't know when the series ends ... . :)

Alhamdulillah hirobbil alamin.



Tercatat
\[ \sum_{j=0}^\infty \frac{1}{j!(n-j)!} = \frac{2^n}{n!} \]

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Re:DIVISION BY 0
« Jawab #2 pada: Juli 19, 2018, 06:36:28 PM »
Benedictus qui venit in nomine Domini.

Kutip dari: river_rat
But one infinite series I do find confusing is $1 - 2 + 3 - 4 + 5 - \cdots$, which apparently sums to $1/4$ !

\[ 1 - 2 + 3 - 4 + 5 - 6 + \cdots \]
\[ = (1 + 3 + 5 + \cdots) - (2 + 4 + 6 + \cdots) \]
\[ = \sum_{j=0}^\infty (2j - 1) - \sum_{j=1}^\infty 2j \]
\[ = -\sum_{j=1}^\infty 1 \]

is negative infinity ... ,

so this series is divergent ... .



I'm sorry if I do mistake ... .  :(

Sampai jumpa lagi.



Tercatat
\[ \sum_{j=0}^\infty \frac{1}{j!(n-j)!} = \frac{2^n}{n!} \]
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