1. "For most of the recurrences we shall examine, it is straightforward to extend boundary conditions to make the inductive assumption work for small n, and we shall not always explicitly work out the details." 2. "You might find the idea of subtracting a lower-order term counter intuitive. After all, if the math does not workout, we should increase our guess, right?"

1. "For most of the recurrences we shall examine, it is straightforward to extend boundary conditions to make the inductive assumption work for small n, and we shall not always explicitly work out the details." 2. "You might find the idea of subtracting a lower-order term counter intuitive. After all, if the math does not workout, we should increase our guess, right?"

The first one is "calculate". "explicitly work out" means "show all the steps of the calculation".

A paragraph like this: "x + 5y = 3 and 2x + y = 9. Therefore, of course, x = 4.667 and y = -0.333"

That doesn't work out the details explicitly - there are five or six steps missing in the middle. Your book probably has more complex examples, though!

************* The second one seems to be "To prove successful, effective, or satisfactory"

I'm not sure of the context, what sort of 'terms' you are working with, but that seems to be the right meaning.

work out 2. (tr) to solve or find out by reasoning or calculation: to work out an answer; to work out a sum.

And in the Oxford.

work out if something works out at something, you calculate that it will be a particular amount The restaurant bill worked out at £23 each. This all works out to around $11 000. + adj. It'll work out cheaper to travel by bus.

work something out to calculate something to work out the answer

Great. Thank you so, so much!!! Sorry Drago, can I please ask this one too?

Sometimes you might correctly guess an asymptotic bound on the solution of a recurrence, but somehow the math fails to work out in the induction. The problem frequently turns out to be that the inductive assumption is not strong enough to prove the detailed bound. If you revise the guess by subtracting a lower-order term when you hit such a snag, the math often goes through.

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