Use set notation, and list all the elements of each set. {1, 1...

Question

Use set notation, and list all the elements of each set. {1, 1/2, 1/4, ...., 1/32} .

Accepted Answer

Welcome back. I am so glad you're here. We are given this set starting with one and then 1/6. 1 36th. And then ellipses to indicate that it keeps going all the way up to one 7776th. And that's the end of our set. More asked to enumerate all the elements. Well that means we have to list everything including what's going on here, within these ellipses, where it just keeps going. So essentially we have to ask ourselves what's the pattern that's going on here. Well, we noticed that going from 1/6 to 1 36 how do we get between those? Will we take 1/6 times? 1/6. Can't say sixth. And that gives us one 36th. So Looking at this pattern, what's actually going on here? The one is actually a 1/6 raised to the zero because anything raised to the zero equals by definition one. So that's 1/1 or just one. That's how we got that one. Well, the 1/6. The next one in our pattern in our set, that's 1/6 to the first. One, 36th. That's 1/6 squared. So what's going on in the ellipsis here? Well, we're just going to keep going with this pattern. That's 1/6 to the third. Well what is that? Okay, so we've got 1, 1/6 1/36 what's 1/6 to the third. Six to the third is 216. So that's one over 216. Alright, how about 1/6 to the fourth. Six to the fourth is to excuse me? Not 3296. So that's one over 1296. Okay, that was 1/6 to the fourth. And now let's see. 1/6 to the fifth. Well, Six to the fifth is 7,776. Ah that's what we had listed at the top as our final number in our set. So this is our set, fully enumerated, including what was going on there in the ellipses. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

Use set notation, and list all the elements of each set. {1, 1/2, 1/4, ...., 1/32} .

Key Concepts

Set Notation

Geometric Sequences

Listing Elements of a Set

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