# log 2=0 ?

• September 8th, 2006, 06:05 AM
sramanujam
log 2=0 ?
A recent post made by one of our forum member proves (?) that 4=5. Questions like this will help us to understand better math deeper and deeper which can never be gained through books or even in class rooms. So in that sense, I'd like to post a thread asking readers to prove it wrong by finding the flaw in it.

log(1+x) is expanded by using maclaurin series to get x-x^2/2+x^3/3-...
By putting x=1, we get, log(1+1)=log(2) = 1 - (1/2) + (1/3) - (1/4)+...

Now, add and subtract RHS by 1/2, 1/4 etc. After rearranging, you will get

1+(1/2)+(1/3)+(1/4) - 2[(1/2)+(1/4)+(1/6)+(1/8)+...]

Multiplying second terms by 2, we get

[1+(1/2)+(1/3)+(1/4)+...] - [1+(1/2)+(1/3)+(1/4)+...]

= 0 (???)
• September 8th, 2006, 12:12 PM
william
Hi sramanujam,
This was asked in the 2nd post in the thread '1=2 'proof'... what's wrong?'.

The quick answer is that the series for ln(2) is conditionally convergent.

I hope I am vague enough to where I didn't spoil the fun for others who may still want to tackle this on their own....

Do you have any others? They are fun to think about!

Cheers,
william
• September 8th, 2006, 11:46 PM
sramanujam
thanks for pointing out to me...
@william
Thanks for pointing me out that. I'll certainly post questions similar to this kind, which helps us to understand math better and deeper.