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How do I show the following:

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,051

It comes readily from the series expansion of log(1+x) and log(1-x)

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,752

Hi;

Run these.

```
Assuming[x != 1,
FullSimplify[
Log[Sqrt[(1 + x)/(
1 - x)]] == (1/2) Log[(1 + x)/(1 - x)] == (1/
2) (Log[1/(1 - x)] + Log[1 + x])]]
```

```
a = Series[Log[1/(1 - x)], {x, 0, 10}] // Normal
b = Series[Log[1 + x], {x, 0, 10}] // Normal
```

`(1/2) (a + b) // Expand`

Now match that up term by term with your series on the LHS.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,051

*Last edited by thickhead (2016-12-25 19:14:40)*

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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Thank you guys

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

**Online**

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