Prove that: $ (a

Question

Prove that: $$ (a<b<c) \implies (a<\frac{a+b+c}{3}<c) $$ I'm having problem proving these implications (I don't know how they're called in English). Can you tell me what I have to read to understand these?

score 7 · Accepted Answer · edited Aug 17 '15 at 16:15

7

HINT:

$a<b<c\implies 3a=a+a+a<a+b+c$

and $3c=c+c+c>c+b+a$

edited Aug 17 '15 at 16:15

Conrado Costa

6,071

answered Aug 17 '15 at 16:11

lab bhattacharjee

274,582

I'm sorry, I don't understand. How did you come up with $a+a+a<a+b+c$? – Gjekaks Aug 17 '15 at 16:34
$a\lt b, a\lt c$ – Eleven-Eleven Aug 17 '15 at 16:35
@Eleven-Eleven oh, yeah! Thanks. – Gjekaks Aug 17 '15 at 16:38

Prove that: $ (a

1 Answers1