Proof of Inequality by Induction

Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
Sign up Log in
1 reply · 2K views
sbrajagopal2690
Messages
2
Reaction score
0
need help on this

Show by induction that n^3 <= 3^n for all natural numbers n.
 

Discussion

Physics news on Phys.org
Re: Proof of Inequlity by Induction

sbrajagopal2690 said:
need help on this

Show by induction that n^3 <= 3^n for all natural numbers n.
Hint: If $n\geqslant 3$ then $(n+1)^3 \leqslant \bigl(n+\frac n3\bigr)^3$.
 

Similar threads

Prove 1/√n Inequality by Induction

  • KOO
  • · Replies 1 ·
  • Set Theory, Logic, Probability, Statistics
Replies
1

Proof of Inequality: Induction & Derivation Help

  • PhysicsRock
  • · Replies 12 ·
  • Precalculus Mathematics Homework Help
Replies
12

Induction Proof of Inequality Involving Summation and Product

  • Reckoner
  • · Replies 5 ·
  • Set Theory, Logic, Probability, Statistics
Replies
5

Proof of Inequality: $|a+b| \leq |a| + |b|$

  • solakis1
  • · Replies 8 ·
  • General Math
Replies
8

Undergrad On Jensen's inequality for conditional expectation

  • psie
  • · Replies 1 ·
  • Set Theory, Logic, Probability, Statistics
Replies
1

Simple proof of inequality by induction

  • naele
  • · Replies 3 ·
  • Calculus and Beyond Homework Help
Replies
3

Proof by induction - Really confused

  • Tvtakaveli
  • · Replies 4 ·
  • Set Theory, Logic, Probability, Statistics
Replies
4

Proving an Inequality by Induction

  • student34
  • · Replies 4 ·
  • Calculus and Beyond Homework Help
Replies
4

Proof by Induction - in Sequences.

  • johnny009
  • · Replies 2 ·
  • Set Theory, Logic, Probability, Statistics
Replies
2

Understanding induction proof of pigeonhole principle

  • Mathmellow
  • · Replies 4 ·
  • Set Theory, Logic, Probability, Statistics
Replies
4