Hint: If $n\geqslant 3$ then $(n+1)^3 \leqslant \bigl(n+\frac n3\bigr)^3$.sbrajagopal2690 said:need help on this
Show by induction that n^3 <= 3^n for all natural numbers n.
"Proof of Inequality by Induction" is a mathematical method used to prove that an inequality is true for all values of a variable by using a specific set of steps and assumptions.
The main difference between "Proof of Inequality by Induction" and regular induction is that regular induction is used to prove statements about whole numbers (usually starting at 1), while "Proof of Inequality by Induction" is used to prove statements about real numbers.
The steps involved in a "Proof of Inequality by Induction" are:
"Proof of Inequality by Induction" is used when trying to prove a statement involving real numbers, such as inequalities, summations, or product formulas.
One potential limitation of using "Proof of Inequality by Induction" is that it can be difficult to find a suitable inductive hypothesis, and if the hypothesis is not strong enough, the proof may fail. Additionally, "Proof of Inequality by Induction" can only be used on statements that involve real numbers, so it may not be applicable in all mathematical scenarios.