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Prove that for all n in the natural numbers 3^n greater than or equal to 1+2^n.

Here's my start:

3^1 greater than or equal to 1+2^1, so the statement is true for n=1.

Assume that for some n, 3^n greater than or equal to 1+2^n

Then 3^n+3^n+3^n greater than or equal to 1+2^n +3^n+3^n.

It follows that 3^(n+1) greater than or equal to 1+2^n+2*3^n.

Where do I go from here? I still need to show that 1+2^n+2*3^n is greater than or equal to 1+2^(n+1)

Thanks!

Here's my start:

3^1 greater than or equal to 1+2^1, so the statement is true for n=1.

Assume that for some n, 3^n greater than or equal to 1+2^n

Then 3^n+3^n+3^n greater than or equal to 1+2^n +3^n+3^n.

It follows that 3^(n+1) greater than or equal to 1+2^n+2*3^n.

Where do I go from here? I still need to show that 1+2^n+2*3^n is greater than or equal to 1+2^(n+1)

Thanks!

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