mathematical induction step 4 (2 Viewers)

[petermik]

I make a different one up every single time I come pass induction LMFAO

 

[asianese]

I remember Carrot making his vast, powerful conclusion of:

 

[Lieutenant_21]

I make a different one up every single time I come pass induction LMFAO

Since the statement is true for n=k and n=k+1 then it is true for n=1, 2, 3, 4, 5... Hence it is true for all integers n>/=1 by mathematical induction.

 

[RealiseNothing]

Since the statement is true for n=k and n=k+1 then it is true for n=1, 2, 3, 4, 5... Hence it is true for all integers n>/=1 by mathematical induction.

You probably won't have marks taken off for this, but it's not correct. If you were to take this approach you'd have to say:

"Since the statement is true for n=k+1, if it is true for n=k, then it is true for n=1, 2, 3, 4, 5... Hence it is true for all integers n>/=1 by mathematical induction."

Because you haven't proven that it is true for n=k. You have only shown that if it is in fact true for n=k, then it is also true for n=k+1. The induction comes into play by first proving it is true for n=1, which then implies it must be true for all integers that follow as in this case k=1.

 

[Lieutenant_21]

You probably won't have marks taken off for this, but it's not correct. If you were to take this approach you'd have to say:

"Since the statement is true for n=k+1, if it is true for n=k, then it is true for n=1, 2, 3, 4, 5... Hence it is true for all integers n>/=1 by mathematical induction."

Because you haven't proven that it is true for n=k. You have only shown that if it is in fact true for n=k, then it is also true for n=k+1. The induction comes into play by first proving it is true for n=1, which then implies it must be true for all integers that follow as in this case k=1.

Thanks for the correction

 

[RealiseNothing]

Thanks for the correction

Oh and I forgot, you should also add in the induction initiation step as well if you are going to say that (ie "it is true for n=1").