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8 6n 2 A n ! 0Find the sum of the series:...

Question

8 6n 2 A n ! 0Find the sum of the series:

8 6n 2 A n ! 0 Find the sum of the series:



Answers

Find the indicated partial sum for each sequence. $$a_{n}=2 n-1 ; S_{8}$$

Three Geometric means that there is some kind of dividing or multiplying happening. And since the numbers are getting larger over time, that means we were probably multiplying by something. And so, if you're not sure what number to multiply by, just doing 12 by two by eight to figure out that constant, um, the common ratio, so 12 divided by heat is 1.5. So you can double check this by doing what's 12 times 1.5 in your calculator and you get 18. So this means our equals 1.5. Now the formula for the sum of a geometric series is s. Some geometric series equals your first term. Times one minus arch The end all over one minus R No, we already hope are you figured that out right here. It's one point point, and it's how many terms there, and it's given to you a one. It's just one is the first number in your sequence. And so now we can put those numbers in to get eight times one minus 1.5 to the eighth power all over one minus 1.5. Type that into my calculator and I get 394.62 fights. This is your answer

In this question we have to find us some of eight plus 88 plus 888. Up to enters given series is eight plus 88 plus hit 888. Okay. Up to in terms just taking Common aid one plus 11 plus 111 plus up to. And towns. Yes multiply and divide my name. 8.9 into nine plus 99 plus 999. Up to in terms Okay 8.9 into then minus one less 100 -1 plus. Mhm 1000 -1 glass questions is up to in terms mhm 8.9 into 10 plus Danny Squire plus. Thank you. Up to and towns minus one plus one plus one plus up to Anton's here, 10 plus 10 X squared plus 10 cube up to interns are NGP becomes the ratio of consecutive terms are constant Your first time with 10. And commonly issue is also 10. Is he kidding 8.9 into turned into 10 to the power and minus one upon then minus Lynn minus and is equal to eight upon nine into 10 to the power 10 plus one minus. Then upon nine minus and mhm Eight upon nine into 10 to the power endless one minus 10 minus nine And upon nine no is equal to eight upon 81 into 10 to the power and plus one minus nine and minus 10 required. Some is equal to eight upon 81 into 10 to the power and plus one minus 9, 10 minus 10. Thank you very much. This is our final answer for this question.

You have our number nine in which we need to find the sum of in terms of. Okay. And this term is being given and squired bliss to raise to the pardon. Okay so some will be equal to submission of any any square from an equal to one to end. Plus the mission of tourists. The power end from an equal to one to end. So this is read about in and square which is some of the sum of the squares of first energy numbers. So and in two and penicillin into 20 plus one by six. Place. There's a tourist department. So too is the power end which means ah we have if you open it it will be too place to a square plus two. Q up to tourists of Power End which is a Gp with oh uh huh. With first time too. In common issue two and into one plus one 21 plus one by six plus. Listen will be two and two tourist to the power and minus one by two minus one. So and in two and plus one 20 plus one by six, plus two and two tours to the Power and minus one. This is the sum. Thank you so much.

We have a number eight. And that's when you defined the some of in. Into. And bless one and plus four. And this is A. M. So let us multiply this and write in simple form. There's a five N. Plus four. So this is an cube plus five and square was foreign. So S. N. Will be equal to an equal to one to end A. N. And if you distribute it will be an equal to one to end and kill less fired and equal to want to end and square plus four an equal to one to end and and N. Cube and into. And bless one by two. Whole square plus five and into. And plus one 20 plus one by six. Because this is some of square of and new Zealanders thus far into N. And to end plus one by two. So this is an into and plus one hold Squire uh by four plus five by six and into one plus one one plus one. And bliss uh Let us do to end and and plus one. Now let us take and in two and plus one as common. You know okay we can take to as well. So this will become an into. And plus one by two bless five by six 21 plus one bless four. That's all. And in two and plus one by two. This is and square place and and Elsom of six. And to his 12. So we should be writing 6263 So this will be three and a square plus three in blessed 10 in plus five bless 24. So this is N into unpleasant by two. And there's a three and a square place 39 blessed 29 26 So as N. Is equal to and into. And bless when the end is squired less 13 and last 29 by 12. But they should be the answers. Thank you so much.


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