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# Proof by Induction help! watch

1. hello, can anybody take a look at this question and solve it?

Base Case : g(0) = 0
Recursive Case : for any x>0 we have g(x) = g(x-1) +2

Prove that the properties hold for g by using induction

g(n) = n+n

this has got me really stumped :\ i have asked other students, and even a friend who is doing a maths degree! but nobody can seem to prove it.

If you can you are a genius and thank you !!
2. (Original post by DaveRawsthorne)
hello, can anybody take a look at this question and solve it?

Base Case : g(0) = 0
Recursive Case : for any x>0 we have g(x) = g(x-1) +2

Prove that the properties hold for g by using induction

g(n) = n+n

this has got me really stumped :\ i have asked other students, and even a friend who is doing a maths degree! but nobody can seem to prove it.

If you can you are a genius and thank you !!
He can't be doing very well in his Maths degree...

Well, do you know what Proof by Induction is?
First write down your Inductive Hypothesis: g(n) = 2n

Then show it holds for the base case. So does the Inductive Hypothesis hold for n = 0?

Then you assume it holds for n = k. So you take it to be true that g(k) = 2k.
Now put in g(k+1) into the recurrence and see if you can show the Inductive Hypothesis is true for then.
3. Thank you !

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