Prove by induction that for all integers n greater than or equal to 2, 2^n+1 < 3^n

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- Dec 12th 2009, 04:39 PMleinadwerdnai struggle with proofs by induction
Prove by induction that for all integers n greater than or equal to 2, 2^n+1 < 3^n

- Dec 12th 2009, 05:36 PMcraig
This is how I would do it:

For , , , true for

Assume for , this gives you

Now the induction step, prove for

Dividing both sides by 2

Therefore if , then is definitely , true for all if true for

True for , therefore true for all integers greater than or equal to 2.

QED - Dec 15th 2009, 03:07 PMleinadwerdna
for the induction step couldnt you also do with 2^(k+1)<3^k multiply both sides by 2 of that so you get 4(2^k) < 2(3^k). And since we are trying to prove 4(2^k)<3(3^k) this obviously proves it since 2 is less than 3

does this make any sense