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Problem #7: Suppcse tnat the %rh partial sum oftne serie:13 - 4SFind &3Find...

Question

Problem #7: Suppcse tnat the %rh partial sum oftne serie:13 - 4SFind &3Find

Problem #7: Suppcse tnat the %rh partial sum oftne serie: 13 - 4S Find &3 Find



Answers

$$\text { Find the indicated partial sums for the sequence.}$$ $$1,2,3,4,5,6,7, \ldots ; S_{3} \text { and } S_{7}$$

For the fourth, partial sum means test for, It's going to take the summation from K equals one or three forth to the K -1. So simplifying this out, that gives us 3/4 to the zero plus 3/4 no one, 3/4 to to straight points to the third, Plug in from 0 to 4. I went to four of you. So then, So that gives us 127 over 48 1 plugged in.

4th, partial. Some of this Means that we're doing from chemicals one before negative for care plus one More breath rate. Okay. Why this one that's going to give us since one In this 1/3. This 1/9. This 1/27 supervised 20 over so.

And the sequence of partial stops and this sequence here, so s one going to be equal to 1/2 times three which is 162 It's too Single to 1 6th plus two or 3 times four which is two times two or 12. So Still also simplifies to 160. Okay, So then has three, it's equal to 1/6 plus 2/12, three over 20 score. It was 16 plus 2/12, 3/20 Plus 4/30, and has five equal to 16 plus 2/12. 3/20. It's 4 30 It's 5/42.

Kind of sequence of partial sums. So we've got that S one 21 over history, age six has two is equal to 1/6 Plus two, or 12 is equal to two or 6. Here She goes 1 3rd Next Best three is equal to one third plus over 20. So that's equal to 29/60, or as for 29/60 plus for over 30 just equal to you, 37/60. Finally, five equal to 37/60 plus 5/42, She goes 103 over 1 40. So that's our sequence of partial subs.


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