Check out some similar questions!

galactus · Feb 17, 2007, 11:23 AM

As you may know, a unit fraction is a fraction with 1 in the numerator.

Can you write 1 as a sum of seven unit fractions? Or even more than 7?

Capuchin · Feb 17, 2007, 11:33 AM

Infinity unit fractions?

$\sum_{n=1}^\infty \frac{1}{2^n} = 1$

galactus · Feb 17, 2007, 11:48 AM

You're so right, Cap, but I just wanted to see something more finite. It's not difficult. I am sure you know how.

.

Capuchin · Feb 17, 2007, 11:50 AM

I know, I'm just trying to be a smart arse. I'll leave it to others to have a go :)

galactus · Feb 17, 2007, 12:34 PM

I think I just spoiled that. Maybe I oughta delete it for now.

BTW, what you done was clever. Showin' off:)

asterisk_man · Feb 17, 2007, 07:54 PM

$\sum_{n=1}^k \frac{1}{k} = 1$

Is there an additional complication that I'm missing?

Capuchin · Feb 17, 2007, 07:56 PM

Yes, the question confused me too, I would think that for many sets of 6 unit fractions you can come up with, you can pick a 7th that will make the sum 1.

Edit: on second thoughts probably not, but it isn't very hard :/

I'm thinking he meant different unit fractions, at least there is a little challenge there.

galactus · Feb 18, 2007, 07:13 AM

Yes, I meant different unit fractions.

You can string it out however far you want to by using:

$\frac{1}{n}=\frac{1}{n+1}+\frac{1}{n(n+1)}$

and keep substituting.

MathMaven53 · Feb 26, 2007, 12:33 PM

1 = 1/2 + 1/2
= 1/2 + (1/2 - 1/3) + 1/3
= 1/2 + 1/3 + 1/6
= 1/2 + 1/3 + 1/7 + (1/6 -1/7)
= 1/2 + 1/3 +1/7 + 1/42
= 1/2 + 1/4 + (1/3-1/4) + 1/7 + 1/42
= 1/2 + 1/4 + 1/7 + 1/12 + 1/42
= 1/2 + (1/4 - 1/5) + 1/5 +1/7 + 1/12 + 1/42
= 1/2 + 1/5 + 1/7 + 1/12 + 1/20 + 1/42
= 1/2 + (1/5 - 1/6) + 1/6 + 1/7 +1/12 + 1/20 + 1/42
= 1/2 + 1/6 + 1/7 + 1/12 + 1/20 + 1/30 + 1/42

go2lilman · Feb 16, 2012, 06:18 PM

3/4 sun