Well, here's another topic I'm horrible at:Induction.

I think I can do bulk-standard induction, but just to make sure tell me if the following example is correct:

1 + 3 + 5 + 7 + .... + (2n -1) = n2, ε Z+

First let us prove this proposition P works for 1:

P(1) = 2(1) - 1 =1

This must equal n2 = 1 .: P(1) is true and works

Now we assume the proposition works for k:

P(k) = K 2

P(K +1) must therefore equal: K2 + (2(K+1) -1) = 2K + 2 -1 = 2K + 1

P(K+1) = (K +1) (K + 1) = K2 + 2K + 1...

Therefore if P(k) is true then P(K+1) is always true proving the propision istrue.

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I'm hoping I got this right. Tell me if I did...

But then how do we do induction with matrices, calculus, geommetric series etc. ??

Can anyone teach me in a easy way (showing all steps) cause I'm as dumb as a bag of rocks!!!

I have tourgentlyknow this for a test, and the textbook just looks too confusing for me! Please try to make it as simple and easy to udnerstand as possible! Thank you!

- Joey