Question
Question 41Give a big-O estimate for f(n) = J6f(4) + 12n?O(nlog; 6O(n? logn)0 O(n?)lo 0(nlog:| 6DNone oflthese |
Question 41 Give a big-O estimate for f(n) = J6f(4) + 12n? O(nlog; 6 O(n? logn) 0 O(n?) lo 0(nlog:| 6 DNone oflthese |
Answers
Use the result of exercise 40 to evaluate the sum and the limit of the sum as $n \rightarrow \infty.$ $$\sum_{i=1}^{n} e^{(6 i) / n} \frac{6}{n}$$
Okay, so we want to find our call information using this equation. So looking at our equation are left inside without to put that information from Isaac. What is their own Teoh on starting or on? Our equation is eight times R to the power of so notice that we have i Z one. So it's very thought in terms of I, um, information, or are starting value as zero so well, but cave equal to I, which is one minus one. So this is what, 21 minus one, which is zero. Okay, so we can rewrite this as some of Casey Cathedral two and minus one of me to the power of six eyes. Now K plus one over and then six over and Phillips break up this time here. You could be right this into eating six K over and plus six over end and using our exponential properties that seek with the easy to six J over. End time. Easy. This X over. Okay, so we get six e tudo six over end over end and cto her of six over end. You're part of K. Okay? I know we can hear it. This oz is a question here. So we have our This is our time and this is our So we have a minus. A times are part of our ending terms. That's a nice one. Plus one. We only have six each of the six over and over. And then my is the same thing. And then we have Beekeeper of six over end to the power of and which is an minus one plus one. So that's the sun over one minus the same thing. We're are really Okay, so we get the fault.
Okay, so we're asked to what end degraded and equal to one and show that if it actually affects this fall, that X plus one too hard won over and box money equals one plus X over and us one might just end over two and sport and excellent to and use this approximation with an antique 62 x s may want five to carve one of six. Okay, so we're gonna take preservative off Lex two times that we have after Lex. Because if you notice we have a degree to here is equal to x one. The power of what? Over end f 01 of a kind of X is one over end times X plus one. Depart one over. And this one time at zero is it puts one over and on. F double time of X is one over end times one over. And this one exports one to fire of one over anymore. To double prime at cell is equal to one over any times. One over end, like this one. OK, it's our terror polynomial into that. Don't at the region is equal to one plus one over end X plus one over and squared when it's one over in X squared over too. Well, that actually just give me what we have over here. Right? So we got what we wanted and now with and is equal to six with a box of faith. 1.5 to crab over six. That's blackmail equal to our Taylor. Following will kneel at your reports. Five plugging up into here. Look at this is approximately equal to three over par 307 over to eight states, which is approximately 1.66
Sequence of defined by a N is equal to four plus three times at number of terms, and we're looking to find some of the 1st 6 terms so we can find the last term by plugging and go six into this creation, get four plus three times 6 18 and 18 plus four is equal to 22 so the last term is 22 we know the first term first term is four plus three times. One is seven, so the first room is seven in the last term is 22. You can plug these values into equation and over to a number of terms divided by two times and parentheses. First term plus last term it's a number of terms is 66 over to is three and seven, plus 22 7 plus 22 is 29 so three times 29 3 Time 29 is equal to 87. So 87 is some of the 1st 6 terms