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Find the sum of the series:09 (~ln-1 2 2 7n n=l...

Question

Find the sum of the series:09 (~ln-1 2 2 7n n=l

Find the sum of the series: 09 (~ln-1 2 2 7n n=l



Answers

Sum up to $n$ terms the series $0.7+0.77+0.777+\ldots$

I'm gonna find out those cities that we have just uh Are you guys like to you one blood You to last you three and so but why not? You too negative? You want. That is 703. 4 For the ball one you can interview too. 43 97. The sport about two. You born in the U. three. That is nearly 87 a reported three. Or the back screen. So we can say Oh um negative you and 31 that leaves or the bark and negative. Right? We just add all this stuff so we add all this all this at each all this stuff equation The U. two candidate YouTube you can reuse three and so on. But we get here U. N. Negative. You won not to be four to the power one plus four by two. It's born blood for the violent and some of the tv that unites customer support foundations for that is greater than one for the bar. We have a negative one negative 1/4 negative one automatically now four times for the n. That is giving worry about a negative war Over three. This to me actually um negative you want to define um here to find out the commission of cities. The U. N. Uh Board of our and negative for over three plus three that is giving for the bar and negative four plus nine. Their report apart. And all the divine over point. The national citizen information is gonna jump for the bar plus 5/3 from article +212. Now to find out I would be one hour three half for the borrower has given a sport about one plus for the bad tube and so on. Plus or the bottom plus you have five times then fighting. So 1/3 times. Did they get a G. P. The ball's coming four common issues for more than one before the bar and negative one or being happy. What? I really wanted this three. What to do? Bye Ben. So you just work on this That's coming out before the park and plus one negative pole or 194 to 5. And over three that has given us started about 10 plus one -4 Plots of Tina. All of them. Now pick it up and long for the new book final are put. Thank you.

Siri's. We had a formal funder s and culture and even invite you. I want Plus, I am on, innit? You this formula with next you need to make so than this one must be understood. Uh, next because you won. So we have to be rendition Engineer Index standing one now. So we reduced the index by three. So the Thomas equal to 17 now and inside we need Thio. Replace the end bind. Uh, And last three now on blast you and then we signify this one Then so we have this one. The seventh in the far Always want to compete and seventh in ankle juniors. 17 different about you The first time, ace when an echo Jew One they wouldn't. Cy, we're going too far Times, uh, Mina's upon a tree on Ben. We're blessed. Thio got wrinkled. You 0.8 and the last time would be any 17. So it was with a 17 in Saigon Uh, trump t times the minister upon a tree and then plus two gonna coach humanists far. And then we should get Geico Jew now 10 17 being writing by Ju we should get equal to minus 27 point for a bunch. You here

In this problem, we're being asked to find the sum for the given geometric series. Well, luckily we have a formula to do this, it's S a Ben is equal to a sub one times one minus are to the end power all getting divided by one minus R. Okay, first, we're gonna find days of one to do this. We're going to substitute zero in place of entering our formula. So I have a size of one equal to two times five. Race to the zero power. Well anything to the zero power is equal to one. So then we'll have two times one, which is just equal to two. Next we have to find our well to do this, we have to find the second term in the series. So to find a set of two, we're gonna substitute in uh one for it. So we're gonna have two times five to the first power. Well, five to the first power is equal to five, and two times five is 10. Great. Now that we know the first two terms we can find our we find our by figuring out two times what is equal to 10. Well two times five is equal to 10, so R. Is equal to five next. We need to find and well we have to be a little careful here. In this case we're starting one and is equal to zero. Typically we start when and is equal to one. So in this case if we were going from 1 to 7 and would be seven. But because we're going from 0 to 7 we have that extra term there, which means N is really equal to eight. Well now we have all the information we need. So we'll just substitute these values into our formula. So of S. F. Eight is equal to a. Someone which is two times one minus R. Which is five raised to the eighth power, all getting divided by one minus five. Now we just need to calculate this so we can actually type in the new Marie there into our calculator. So you can do to open parentheses one minus five to the eighth power and then our denominator. We have one minus five which is negative for. So we can divide this value by negative for so the some of the series is 195,312 right.

The first thing you should see when you look at this question is this summation which is the sigma sign of n equals one to n equals seven of the function to end plus one so formal you have to use as we've been using for all arithmetic. Summations is and over to times ace of one plus a seven is equal toe s ev en. So we have end here, which is equal to seven divided by two times, two times one plus one. So that's two plus one plus two times seven plus one was just 15. That's 18. So now what do we know? 18 divided by two times seven should be 63 because that's when nine times seven is so 63 is the final summation of n equals one to n equals seven of the function to end plus one


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