/sci/ - Science & Math » Thread #14426045

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Anonymous Mon 25 Apr 2022 03:38:11 No.14426045 View Reply Original Report

Quoted By: >>14426083 >>14426085 >>14427035 >>14427553 >>14427562 >>14429823

How do you prove this is true for every combination of x and y? All variables in the equation are integers.

Anonymous

Anonymous Mon 25 Apr 2022 03:46:07 No.14426061 Report

Quoted By: >>14426076

LCD(a,b,...,N) = y
Then the harmonic sum of (a,b,...,N) is equal to x/y for some integer x.
QED

Anonymous

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Anonymous Mon 25 Apr 2022 03:53:24 No.14426076 Report

Quoted By: >>14426077

>>14426061
LCD is a liquid crystal display. Dunno what that has to do with math

Anonymous

Anonymous Mon 25 Apr 2022 03:54:13 No.14426077 Report

Quoted By:

>>14426076
Typed this math on a liquid crystal display

Anonymous

Anonymous Mon 25 Apr 2022 03:56:19 No.14426083 Report

Quoted By:

>>14426045
https://en.wikipedia.org/wiki/Rational_number#Addition

Anonymous

Anonymous Mon 25 Apr 2022 03:57:30 No.14426085 Report

Quoted By:

>>14426045
Is n actually n so there are 14 drains added on the right side or how many are there?

Anonymous

Anonymous Mon 25 Apr 2022 13:38:20 No.14427035 Report

Quoted By: >>14427685

>>14426045
I couldn't even get $\frac{2}{1}$ from $\frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{50}{24} = 2.0833333333333335$

Anonymous

Anonymous Mon 25 Apr 2022 17:08:42 No.14427553 Report

Quoted By:

>>14426045
a,b,c, n should be z1, z2, z3, zn
z = y and x = n

Anonymous

Anonymous Mon 25 Apr 2022 17:10:46 No.14427562 Report

Quoted By: >>14427595

>>14426045
$\frac{x}y = \underbrace{\frac1y + \frac 1y \ldots +\frac 1y}_{x\textrm{ times}}$

Anonymous

Anonymous Mon 25 Apr 2022 17:10:49 No.14427563 Report

Quoted By:

Induction on n.

Anonymous

Anonymous Mon 25 Apr 2022 17:22:00 No.14427595 Report

Quoted By:

>>14427562
you are minimal fun

Anonymous

Anonymous Mon 25 Apr 2022 17:31:07 No.14427627 Report

Quoted By:

$x = y/a+y/b+y/c+...y/n$ ?

Anonymous

Anonymous Mon 25 Apr 2022 17:51:04 No.14427685 Report

Quoted By: >>14429445

>>14427035
the proof does not stipulate that the sum must be a harmonic series, merely that the variables be integers

2/1 = 1/1 + 1/1 = 1/1 + 1/2 + 1/2 = 1/2 + 1/2 + 1/2 + 1/2 = ...

Anonymous

Anonymous Tue 26 Apr 2022 03:39:47 No.14429445 Report

Quoted By: >>14429599

>>14427685
no, I wasn't trying to make harmonic series
a, b and c are variables and they shouldn't share the same value
$\frac{1}{1} + \frac{1}{1}$ is $\frac{1}{a} + \frac{1}{a}$ not $\frac{1}{a} + \frac{1}{b}$

Anonymous

Anonymous Tue 26 Apr 2022 04:34:33 No.14429599 Report

Quoted By:

>>14429445
Fine then, be a stickler about it, you can get 2 from a 1/2^n series

a = 1
b = 2
c = 4
d = 8
etc

Anonymous

Anonymous Tue 26 Apr 2022 06:49:21 No.14429823 Report

Quoted By:

>>14426045
use induction see usamo (between 197x to 198x, forget which year) for idea how to tackle problem like this

also related is IMO1992 problem 6, IMO2012 problem 6

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