- #1
naele
- 202
- 1
Homework Statement
Prove that [tex]n^3 \leq 3^n[/tex] for [itex]n=1,2,...[/itex]
Homework Equations
Binomial theorem
The Attempt at a Solution
Check for P(1)= [tex]1^3 \leq 3^1[/tex]. So the base case holds, now assume P(k) is true and show that it implies P(k+1).
By assumption [tex]3\cdot k^3 \leq 3\cdot 3^n[/tex]. And this is where I get stuck because obviously [tex](k+1)^3 \nleq 3k^3[/tex]