Suppose $a, b$ are positive real numbers. Then $\frac{a^n + b^n}{2} \ge \left(\frac{a+b}{2}\right)^n$ for any $n$ ∈ $\mathbb{N}$ \ {$0$}.
How should I prove the above statement by mathematical induction? I am stuck in the step in proving $P(k+1)$.
Asked
Active
Viewed 31 times
0
-
How far did you get in the inductive $P(k+1)$ step? – Arthur Apr 28 '20 at 09:43
-
Its a good way to start with the right-hand side and evaluate it. – Wuestenfux Apr 28 '20 at 09:45
-
@Arthur I tried to start from the RHS but I'm not sure how to continue... I tried to multiply (a+b)/2 to both sides of P(k). – Nat Apr 28 '20 at 09:50
