AYMC Intro to Inequalities

• arithmetic sequence (AS)

• arithmetic mean (AM)

• geometric mean (GM)

• harmonic mean (HM)

• quadratic mean (GM)

• arithmetic mean (AM)

• geometric mean (GM)

• geometric sequence (GS)

• this is not a part of the Cauchy-Schwarz Inequality

• 0

• 1

• 2

• 3

• harmonic mean (HM)

• geometric mean (GM)

• arithmetic mean (AM)

• harmonic sequence (HS)

True or False: GM≥AM≥HM

• True

• False

Which one is true?

• HM≥AM≥GM

• AM≥HM≥GM

• GM≥HM≥AM

• AM≥GM≥HM

What can these inequalities help you do?

• Prove certain algebraic equations

• Find minimums and maximums for algebraic expressions

• Both!

When using AM, GM, and HM, what must be true?

• The numbers used must be rational

• There are no restrictions

• The numbers used must be nonnegative, real numbers

• The numbers must be irrational

In the Cauchy-Schwarz Inequality, what must be true about those two sets of numbers?

• They must be integers

• They must be real

• They must be positive

• They have no restricitons