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Ok, I think I got most of the steps covered on these problems but can't seem to get the last part correct:
sorry, image from maple since i still have not grasp on doing the html for the symbols
i don't know if im doing the last steps correctly or not as the other problems without the summation and factorials worked fine.
Attachment 19898
In the second last line, you write, whereas the right-hand side should be
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A style remark. In the beginning of the induction step, you write, "If p(k) is true for all integers k >= 2, then p(k+1) is true". First, it's helpful to write if this is your goal to prove or if you have already shown it. Second, this sentence can be interpreted as, which is trivial. It is better to say, "For all k >= 2, if p(k), then p(k+1)" or "p(k) implies p(k+1) for all k >= 2".
ok i understand that part now. so the second problem should have be [(k+1)!-1]+(k+1)(k+1!). how do you simply this and the first problem to show that they equal p(k+1)?Quote:
Originally Posted by emakarov
In the second last line, you write
A style remark. In the beginning of the induction step, you write, "If p(k) is true for all integers k >= 2, then p(k+1) is true". First, it's helpful to write if this is your goal to prove or if you have already shown it. Second, this sentence can be interpreted as
[(k+1)!-1]+(k+1)(k+1!) = (k + 1)! * (1 + k + 1) - 1 = (k+2)! - 1. In the first problem you similarly factor outQuote:
so the second problem should have be [(k+1)!-1]+(k+1)(k+1!). how do you simply this and the first problem to show that they equal p(k+1)?
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