SOLUTION: I'm having difficulty solving an exercise. The question is: Prove 3^n >=1+2*n. (proving by induction) Basis step is true n=1 3^1>=1+2*1 I assume n=k

Algebra ->  Proofs -> SOLUTION: I'm having difficulty solving an exercise. The question is: Prove 3^n >=1+2*n. (proving by induction) Basis step is true n=1 3^1>=1+2*1 I assume n=k       Log On


   

Question 1022193: I'm having difficulty solving an exercise.
The question is:
Prove 3^n >=1+2*n. (proving by induction)
Basis step is true n=1 3^1>=1+2*1
I assume n=k is true 3^k>=1+2*k
I now have to prove for n=k+1 ; 3^k+1>=1+2(k+1)
3^k*3^1>=1+2*k+2
This is where I get stuck.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Assume induction hypothesis true for n = k, where :

You want to prove that:


First, you can note that , and this is greater than or equal to by induction hypothesis. So


We also know that since .

Therefore



So the statement is true for n = k+1.