Question

what is the 89th odd positive integer

Answer 1

For evens this would be easy, right?!

So, for \(k = 1,2,3,...\), the even no's are 2k. Ie they are: \( 2 * 1 = 2, 2* 2= 4, 2*3 = 6,....\). So, for example, 21st even number is \(2 * 21 = 42\).

For the odds, subtract 1, ie for \(k = 1,2,3,...\), the odds are 2k-1. so they are: \( (2 * 1) - 1 = 1, (2* 2) - 1 = 3, (2*3) - 1 = 5,....\)

Then, if you're convinced by that, the 89th odd occurs at k = 89 and is \((2 *89) - 1 = \dots \dots \)

Idea is really important, say, for series notation.