Number Series - silly

Victor

As a six year old I cut up a square slice of cheese into half, I then ate one half. I then cut the other half in two, I ate one and cut the other in two and so on. I realised that (1/2 +1/4 +1/8 +1/16 .... +1/2^n) =~ 1 (I didn't have the terminology at the time).

So I was dreaming the other night about number series. :rolleyes: But being asleep, I couldn't add (1/3 +1/9 +1/27 ...), but when I woke I did a little spread sheet and

(1/3 +1/9 +1/27 +1/81 .... +1/3^n) =~ 0.5 (not .66666)

Then I tried it with 1/4 and 1/5 and so on and realised that

(1/x +1/x^2 +1/x^3 .... +1/x^n) =~ 1/(x-1), where x>1

I don't remember if we did this in school, I just think it odd that I was trying to work it out in my sleep.

[Edited to corest "1/(x+1)" to "1/(x-1), where x>1". Thank you bonkey.]

bonkey

Originally posted by Victor
Then I tried it with 1/4 and 1/5 and so on and realised that

(1/x +1/x^2 +1/x^3 .... +1/x^n) =~ 1/(x+1)

I don't remember if we did this in school, I just think it odd that I was trying to work it out in my sleep.

Must have been in your sleep - you got it wrong

The sum is asymptotic to 1/(x-1) and not to 1/(x+1).

Think about it. The first element is 1/x, so your total cannot be 1/(x+1)

jc