# Math Help - mathematical induction

1. ## mathematical induction

Prove that $3^n \geq 3n$.
If $n=1$, then $3^1=3(1)$. Clearly, this is true.
Assume $n=k$ and $3^k \geq 3k$.
If $n=k+1$, then $3^{k+1}=3^k 3$
I am stuck here. Can someone explain how to show $3^{k+1} \geq 3(k+1)$? Thank you.

2. Originally Posted by dori1123
Prove that $3^n \geq 3n$.
If $n=1$, then $3^1=3(1)$. Clearly, this is true.
Assume $n=k$ and $3^k \geq 3k$.
If $n=k+1$, then $3^{k+1}=3^k 3$
I am stuck here. Can someone explain how to show $3^{k+1} \geq 3(k+1)$? Thank you.
note that $k \ge 1$, so that

$3^{k + 1} = 3 \cdot 3^k \ge 3 \cdot 3k > 3k + 3k \ge 3k + 3 = 3(k + 1)$