Hello, adkinsjr!
Consider the expansion ofProve the following:
If is a positive integer, then is divisible by 6.
. .
Then: .
. . . . . . . . . .
Hence, is a multiple of 6.
Therefore, is divisible by 6.
I want to prove the following theorem:
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If is a positive integer, then is divisible by 6.
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The only idea I have so far is the following equation:
Where is an infinite sequence:
The sequence doesn't have a common ratio, however I have observed the following:
So it seems that
I'm not really sure if the limit is useful or not.
Ok, I understand this. But how did you develop the idea of expanding the binomial? When ever I go to prove theorems like this, I'm not sure where to begin. You're proof just isn't something I would have noticed immediately.
What particular branch of mathematics should I study in order to obtain this skill?
I am not the one that helped you with your proof, but I am a Mathematics major. Depending on how far you plan to go with developing proofs, you may want to take Discrete Math. If you plan to pursue a career in Mathematics you may want to take something like Foundations of Mathematics. The college you attend may call it something else, but it will be a class strictly on writing proofs. Talk to your adviser and find out what the best classes to take relating to your major.
Hope you find what you are looking for!