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# question 6

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1. http://files.physicsandmathstutor.co...%20Edexcel.pdf
what ending statement can use to complete the induction?

so far i have

if true for n=k then true for n=k+1

since true for n=1 it must be true for n=2,3,4....
and true for all positive integers

is that right? or does putting a limit in of make a difference?
2. (Original post by jakaloupe)
http://files.physicsandmathstutor.co...%20Edexcel.pdf
what ending statement can use to complete the induction?

so far i have

if true for n=k then true for n=k+1

since true for n=1 it must be true for n=2,3,4....
and true for all positive integers

is that right? or does putting a limit in of make a difference?
All you need to say is "true for n=k => true for n=k+1 so since true for n=1, it is true by induction for all positive integers n."
3. (Original post by jakaloupe)
http://files.physicsandmathstutor.co...%20Edexcel.pdf
what ending statement can use to complete the induction?

so far i have

if true for n=k then true for n=k+1

since true for n=1 it must be true for n=2,3,4....
and true for all positive integers

is that right? or does putting a limit in of make a difference?
That's all fine because let's say n=1. Then we know is it is true for n=k+1 so it is true for n=2. But if we let n=2, then we k ow it is true for k+1 so it is true for n=3. This can be repeated indefinitely. That is why the method of induction can prove results of the natural numbers.
4. (Original post by HapaxOromenon3)
All you need to say is "true for n=k => true for n=k+1 so since true for n=1, it is true by induction for all positive integers n."
(Original post by B_9710)
That's all fine because let's say n=1. Then we know is it is true for n=k+1 so it is true for n=2. But if we let n=2, then we k ow it is true for k+1 so it is true for n=3. This can be repeated indefinitely. That is why the method of induction can prove results of the natural numbers.
ok thanks all

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