How Can I Correctly Apply Induction to Solve My Discrete Math Homework?

[phenom01]

Homework Statement

Homework Equations

I need to prove this by using induction. I need help with the induction step.

The Attempt at a Solution

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Basis step: let n=0; 2^0 = 2^(0+1) - 1 -----> 1=1

 

[micromass]

So, what did you try for the induction step?

 

[phenom01]

So, what did you try for the induction step?

i tried sum(2^k+1) = 2^n+1 + sum(2^k)

sum(2^k) = (2^n+1) -1 by our inductive hypothesis

(2^n+1)-1 + 2^n+1

2^n+1 + 2^n+1 = 2^n+2 which gives (2^n+2)-1

I think this is wrong

 

[ideasrule]

i tried sum(2^k+1) = 2^n+1 + sum(2^k)

sum(2^k) = (2^n+1) -1 by our inductive hypothesis

You can't use what you're trying to prove inside your proof.

Try starting out let this: suppose God has told you that the hypothesis holds for n-1. Based off this assumption, can you prove that it also holds for n?

That's your induction step.

 

[epenguin]

It's not exactly wrong in fact you seem to have got more or less the right result, but you have set out a series of formulas and math is not a series of formulas, even when they're the right formulas, it's an argument.

Once you start the formulas you haven't mentioned sum and k any more.

Look up in your textbook how an induction argument is set out and do it the same way rather rigidly and it should work (the algebraic formula calculation part of it is quite simple).