Example of Proof by Induction 4 - Hard Inequality

Real Analysis: Consider the recursive sequence a_1 = 0, a_n+1 = (1+a_n)/(2+a_n). Prove using induction that a_n is increasing. This problem is used in a example of the Monotone Convergence Theorem.

[MathDoctorBob]

Same argument. In the induction step, assume statement n-1 to prove statement a_n.

Yes, where ever you see an n+1, change it to n-1

[ShokoDemon]

how would the induction differ if it was a_n+1 and a_n instead? can i redefine my function, which is given via a_n+1 :=. to be defined as a_n-1 ?