Question

PLEASE PLEASE HELP!!! VERY VERY URGENT!!

i) Prove that the arithmetic mean of two positive numbers must be at least as large as their geometric mean.

ii) Prove that the sum to infinity of a geometric series, all of whose terms are positive, must be at least four times as great as the second term.

iii) Show that if x, y and z are in arithmetic progression, then 10^x, 10^y and 10^z are in geometric progression.


Please explain all answers so I will be able to answer similar questions in the future.

Thank you!

Answer 1

wow !
i would like to help with this one :D
still there ?

Answer 2

yes!
Thank you!

Answer 3

ok lets start :)
Prove that the arithmetic mean of two positive numbers must be at least as large as their geometric mean.

Answer 4

its called the inequality of arithmetic and geometric means..

Answer 5

I haven't heard of that before sorry...this is part of the independent learning part of the syllabus