Math Problem Statement

Prove that 2^n ≥ n^2 for every real number n ≥ 9 using mathematical induction.

Solution

The image shows a mathematical statement that reads:

2nn2,untuk setiap bilangan real n92^n \geq n^2, \quad \text{untuk setiap bilangan real } n \geq 9 which translates to:

"Prove that 2nn22^n \geq n^2 for every real number n9n \geq 9 using mathematical induction."

Proof by Mathematical Induction

We need to prove that 2nn22^n \geq n^2 holds for all n9n \geq 9.

Step 1: Base Case

For ( n =

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Math Problem Analysis

Mathematical Concepts

Exponential Growth
Quadratic Growth
Mathematical Induction

Formulas

2^n ≥ n^2

Theorems

Mathematical Induction

Suitable Grade Level

High School to College Level