Question 26 I In Exercises 1–7, is a sequence or a series given?11+ ...5420.1. 22+42 + 62 + 8² + ...2. 22,42, 6, 8², ...3. 1,-2, 3,-4,5,...4. 1+2,3+4,5+6,7+8, ...5. 1-2+3-4+5 - ..18121.+ ..00(-1)"22.23.22nn=2n=16. 1+2+3+4+5+6+7+8+ ….7. -S, + S, – S3 + S4 – S; + .….I In Exercises 24-27, say how many terms are in the finite ge-ometric series and find its sum.In Exercises 8-18, decide which of the following are geo-metric series. For those which are, give the first term andthe ratio between successive terms. For those which are not,explain why not.24. 2+2(0.1) + 2(0.1)² + … + 2(0.1)2525. 2(0.1) + 2(0.1)² + -… + 2(0.1)'08. 5-10+20 – 40 + 80 – ..26. 2(0.1)5 + 2(0.1)6 + .. + 2(0.1)3119. 2+1+227. 8+4+2+1+21+ .…· +210++..1. 1+21+..I In Exercises 28-30, find the sum of the infinite geometricseries.10. 1+311. 1+x+2x² + 3x³ +4x + ...1. 112. 1-28. 36 + 12 +4+44++ ...4+8.+ ..1613. 3+3z + 6z2 +9z3 + 12z + ….14. 1+2z + (2z)² + (2z)³ + .….29. -810 +540 - 360 +240 – 160 + ….80+ 40 +4030. 80 +20+20++ ...15. 1- y+ y - y + …..V216. 1- x+ x² x' + x* – ...I In Exercises 31–34, find a closed-form for the geometric se-ries and determine for which values of x it converges.17. z-z+ z8 – z'6 + ...18. y +y + y +y + •…000031. (5x)"32. (1– x)"I In Exercises 19-23, state whether or not the series is geo-metric. If it is geometric and converges, find the sum of then=0n=000series.(1 – x/2)"(1- x/3)"34. T0033.119.16+2764+...81n=0n=039+118516110415++11814 -|0117+

To Find: Sum of- 2(0.1)5+2(0.1)6+ .... + 2(0.1)13 NOTE :For r≠1, the sum of the first n+1…

Answered: 26. 2(0.1)5 + 2(0.1)6 + -…- +2(0.1)13

Math

Calculus

26. 2(0.1)5 + 2(0.1)6 + -…- +2(0.1)13

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section: Chapter Questions

Problem 23RE: Use the formula for the sum of the first ii terms of an arithmetic series to find the sum of the...

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Question

Question 26

I In Exercises 1–7, is a sequence or a series given?
1
1
+ ...
54
20.
1. 22+42 + 62 + 8² + ...
2. 22,42, 6, 8², ...
3. 1,-2, 3,-4,5,...
4. 1+2,3+4,5+6,7+8, ...
5. 1-2+3-4+5 - ..
18
1
21.
+ ..
00
(-1)"
22.
23.
22n
n=2
n=1
6. 1+2+3+4+5+6+7+8+ ….
7. -S, + S, – S3 + S4 – S; + .….
I In Exercises 24-27, say how many terms are in the finite ge-
ometric series and find its sum.
In Exercises 8-18, decide which of the following are geo-
metric series. For those which are, give the first term and
the ratio between successive terms. For those which are not,
explain why not.
24. 2+2(0.1) + 2(0.1)² + … + 2(0.1)25
25. 2(0.1) + 2(0.1)² + -… + 2(0.1)'0
8. 5-10+20 – 40 + 80 – ..
26. 2(0.1)5 + 2(0.1)6 + .. + 2(0.1)3
1
1
9. 2+1+
2
27. 8+4+2+1+
2
1
+ .…· +
210
+
+..
1. 1
+
2
1
+..
I In Exercises 28-30, find the sum of the infinite geometric
series.
10. 1+
3
11. 1+x+2x² + 3x³ +4x + ...
1. 1
12. 1-
28. 36 + 12 +4+
4
4
+
+ ...
4
+
8.
+ ..
16
13. 3+3z + 6z2 +9z3 + 12z + ….
14. 1+2z + (2z)² + (2z)³ + .….
29. -810 +540 - 360 +240 – 160 + ….
80
+ 40 +
40
30. 80 +
20
+20+
+ ...
15. 1- y+ y - y + …..
V2
16. 1- x+ x² x' + x* – ...
I In Exercises 31–34, find a closed-form for the geometric se-
ries and determine for which values of x it converges.
17. z-z+ z8 – z'6 + ...
18. y +y + y +y + •…
00
00
31. (5x)"
32. (1– x)"
I In Exercises 19-23, state whether or not the series is geo-
metric. If it is geometric and converges, find the sum of the
n=0
n=0
00
series.
(1 – x/2)"
(1- x/3)"
34. T
00
33.
1
19.
16
+
27
64
+...
81
n=0
n=0
39
+
118516
110415
+
+
118
14 -|0
117
+

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