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Proving inequalities - Does induction work??
prove that, for a,b,c>0, a+b+c=1, 1/a+1/b+1/c≥9
it says that i might want to use the fact that for all X=/=0, X+1/X ≥ 2
using the tip I could make it:
a+1/a+b+1/b+c+1/c ≥ 10
but that's as far as I got.
prove using induction (or anything else):
|sin(nx)|≤n|sin(x)|
for natural n
well it's true for n=1
after using the induction assumption I made it so I have to prove that:
|sin(x(n+1))|≤|sin(nx)| + |sin(x)|
now I'm suck, I don't see how I could use trigonometry equivalences since they all give me cosins and sins*cosins and stuff like that, and these absolute values are a pain aswell, I could square it here and there, to get rid of them, but I don't see where it's going again.
Homework Statement
prove that, for a,b,c>0, a+b+c=1, 1/a+1/b+1/c≥9
Homework Equations
it says that i might want to use the fact that for all X=/=0, X+1/X ≥ 2
The Attempt at a Solution
using the tip I could make it:
a+1/a+b+1/b+c+1/c ≥ 10
but that's as far as I got.
Homework Statement
prove using induction (or anything else):
|sin(nx)|≤n|sin(x)|
for natural n
Homework Equations
The Attempt at a Solution
well it's true for n=1
after using the induction assumption I made it so I have to prove that:
|sin(x(n+1))|≤|sin(nx)| + |sin(x)|
now I'm suck, I don't see how I could use trigonometry equivalences since they all give me cosins and sins*cosins and stuff like that, and these absolute values are a pain aswell, I could square it here and there, to get rid of them, but I don't see where it's going again.