Difference between revisions of "User:Superagh"
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if <math>r=0</math>, | if <math>r=0</math>, | ||
− | <math>P(r)=a_1^ | + | <math>P(r)=a_1^{w_1} a_2^{w_2} a_3^{w_3} . . . a_n^{w_n}</math>. |
if <math>r \neq 0</math>, | if <math>r \neq 0</math>, |
Revision as of 16:39, 24 June 2020
Contents
Introduction
Ok, so inspired by master math solver Lcz, I have decided to take Oly notes (for me) online! I'll probably be yelled at even more for staring at the computer, but I know that this is for my good. (Also this thing is almost the exact same format as Lcz's :P ). (Ok, actually, a LOT of credits to Lcz)
Algebra
Problems worth noting/reviewing
I'll leave this empty for now, I want to start on HARD stuff yeah!
Inequalities
We shall begin with INEQUALITIES! They should be fun enough. I should probably begin with some theorems.
Power mean (special case)
Statement: Given that ,
where
. Define the
as:
where
, and:
where
.
If , then
Power mean (weighted)
Statement: Let be positive real numbers. Let
be positive real numbers ("weights") such that
. For any
,
if ,
.
if ,
.
If , then
. Equality occurs if and only if all the
are equal.