Can Inductive Steps Prove Inequalities in Mathematical Induction?

[Jamin2112]

Homework Statement

So my question i ...

Homework Equations

... when you're trying to prove some inequality, ...

The Attempt at a Solution

... for example, a_n < b_n, can you do the inductive step by doing legal stuff to both sides of the inequality until you arrive at a_n+1 < b_n+1?

 

[╔(σ_σ)╝]

My answer is...
what... is...
legal stuff ? XD ;-)

Do you have a specific example of what you mean ?

 

[Jamin2112]

My answer is...
what... is...
legal stuff ? XD ;-)

Do you have a specific example of what you mean ?

I'm trying to prove that x_n < x_n+1, where x₁ = √2 and x_n+1 = √(2 + x_n)