How to set out Induction proofs?

[SpanishPear]

Hi,
I was just wondering what the "correct" way to set out induction proofs were, especially in regards to the last step/line. My teacher has given us the following steps to set out inductive proofs:

Step 1:      Prove statement true for n = 1. (in most cases)
Step 2:      Suppose statement true for n = k.
Step 3:      Prove statement true for n = k+1, given statement for n = k is true.
Step 4:      Thus, if the statement is true for n = k, it is true for n = k+1. It has been shown that the result is true for n=1, hence , it is correct for n=2.  It is therefore correct for n=3 and so on for all positive integers n.

The issue for me is that step 4 is very time consuming. In the ATAR NOTES headstart lecture slides, it said to use the line "therfore, the result is true by induction" instead. Is there any official way to do it (as required by NESA/markers) to get maximum possible marks? I really dont fancy the idea of writing 50 words at the end of every induction question...

Thanks!!

[RuiAce]

Hi,
I was just wondering what the "correct" way to set out induction proofs were, especially in regards to the last step/line. My teacher has given us the following steps to set out inductive proofs:

Step 1:      Prove statement true for n = 1. (in most cases)
Step 2:      Suppose statement true for n = k.
Step 3:      Prove statement true for n = k+1, given statement for n = k is true.
Step 4:      Thus, if the statement is true for n = k, it is true for n = k+1. It has been shown that the result is true for n=1, hence , it is correct for n=2.  It is therefore correct for n=3 and so on for all positive integers n.

The issue for me is that step 4 is very time consuming. In the ATAR NOTES headstart lecture slides, it said to use the line "therfore, the result is true by induction" instead. Is there any official way to do it (as required by NESA/markers) to get maximum possible marks? I really dont fancy the idea of writing 50 words at the end of every induction question...

Thanks!!

The thing is that for the internal assessments, some teachers are fussy about it and force you to write the very long paragraph.

For the final exam, you can get away by just saying "therefore the result is true by induction"

[SpanishPear]

The thing is that for the internal assessments, some teachers are fussy about it and force you to write the very long paragraph.

For the final exam, you can get away by just saying "therefore the result is true by induction"

Awesome,
Thanks for the update