thesaurus.maths.org

aakkosellinen | kuvagalleriat | otsikot | Nopea haku: vie tämä m-pikakuvake linkkikokoelmaasi

Arithmetic mean - geometric mean inequality | AM-GM inequality (englanti)

Etsi sanaa " Arithmetic mean - geometric mean inequality " OR " AM-GM inequality " NRICH | PLUS | maths.org | Googlella

√

≤ (x+y)/2,

or more generally, for n,m integers we have

(xⁿ y^m )^[1/(m+n)] ≤

nx+my

n+m

The AM-GM inequality states that

n
∑
i=1

a_i

≥

n 
√

n
∏
i=1

a_i

i.e. the arithmetic mean of a set is always greater than or equal to its geometric mean.