Question
Express the sum in sigma notation. 19) 1 5 4+16- 64 + 256
Express the sum in sigma notation. 19) 1 5 4+16- 64 + 256
Answers
Use sigma notation to write the sum. $$\frac{1}{4}+\frac{3}{8}+\frac{7}{16}+\frac{15}{32}+\frac{31}{64}$$
Hello. There are good If you're going to start problem number 62 from the Cuban sequence, we can write expression as minus lor Hold up over and plus learn they were But do is to it for a greater than or equal to block for you The motivation we can write hidden incurred one for seven minus one holding a bowl and plus one different but grooves on the bullet.
In discussion. We need to right the given some as the sigma notation. So the given some is two plus four plus eight plus 16 plus 32 plus 64. As we can see the terms of this some The powers of two. So this can be written as To the power one Plus four can be written as two to the power to Plus 8. 10 million is To the power three 16 can be organized to to the powerful plus 32. Again with an S. Two to the power of five Plus 64 can be written as 2 to the Power six. Now the Powers of to the experience of two is increasing by one in each succeeding term. So the general term general trump for this some kind of a little less 2 to the Power Key. We're case Wearing from 1- six all the integral values. So this submission can be written as sigma notation as submission of 2 to the power. Okay, we are case from 12 six. So this sum is in the form of sigma notation. I hope all of you go discussion. Thank you.
Yes. Let's start rewriting the following in signal notation. Well, let's first notice that we have alternating signs. You have a minus a plus or minus. And of course, for first time. And it's not that we have to for first term And in a poor for a second term, four is two squared, and we have eight. This is too cute, so we can see a pattern. Here. Does this stupid, hard one. So we have, um, negative won t to the power of and plus one. Since we want our first time, that is gonna stick with one to be positive. And we're gonna have divided by two to depart. And we see there are less term. Well, what is 128? Well, that's, um, let's see. That's a two feet of our seven. So are seven is the last time
Okay, so let's note that we have 1/2 1/4 and won over eight, and we have an alternating sign. So it's not that to its due to carve one for 6 to 8 is choosing a power of three. Okay, so we can rewrite this as 1/2 years old. So our summation that would start it's all right, because we have to see crowds. Oh, so that's the end. Be equal to zero. But in fact, you to the part of end, and we end us when to depart of on sick wid 64. Well, 64 is CEO to your size. A base of two sets to do her six. So comparing our exponents, you see that one? Must be good. Six. So that's our last term. Okay, so this is our summation.