a
To find :The third partial sum of the series ∞∑i=12(13)i .
a

Answer to Problem 90E
2627
Explanation of Solution
Given series: ∞∑i=12(13)i
Calculation:
Given series can be written as
∞∑i=12(13)i=2(13)+2(13)2+2(13)3+2(13)4+......
We know that nth partial sum of a series is the sum of first n terms of the series.
Therefore, the third partial sum of given series is
S3=2(13)+2(13)2+2(13)3
which is a geometric series of 3 terms with first term a=23 and common ratio r=13 .
The sum of n of a geometric series with first term a and common ratio r is
Sn=a(1−rn)1−r
Therefore, the third partial sum of given series is
S3=23(1−(13)3)1−13=23(1−127)23=2627
b
To find :The fourth partial sum of the series ∞∑i=12(13)i .
b

Answer to Problem 90E
8081
Explanation of Solution
Given series: ∞∑i=12(13)i
Calculation:
The fourth partial sum of given series is
S4=2(13)+2(13)2+2(13)3+2(13)4S4=23(1−(13)4)1−13=23(1−181)23=8081
c
To find :The fifth partial sum of the series ∞∑i=12(13)i .
c

Answer to Problem 90E
242243
Explanation of Solution
Given series: ∞∑i=12(13)i
Calculation:
The fifth partial sum of given series is
S5=2(13)+2(13)2+2(13)3+2(13)4+2(13)5S5=23(1−(13)5)1−13=23(1−1243)23=242243
Chapter 9 Solutions
EBK PRECALCULUS W/LIMITS
- The Cartesian coordinates of a point are given. (a) (-8, 8) (i) Find polar coordinates (r, 0) of the point, where r > 0 and 0 ≤ 0 0 and 0 ≤ 0 < 2π. (1, 0) = (r. = ([ (ii) Find polar coordinates (r, 8) of the point, where r < 0 and 0 ≤ 0 < 2π. (5, 6) = =([arrow_forwardThe Cartesian coordinates of a point are given. (a) (4,-4) (i) Find polar coordinates (r, e) of the point, where r > 0 and 0 0 and 0 < 0 < 2π. (r, 6) = X 7 (ii) Find polar coordinates (r, 8) of the point, where r < 0 and 0 0 < 2π. (r, 0) = Xarrow_forwardr>0 (r, 0) = T 0 and one with r 0 2 (c) (9,-17) 3 (r, 8) (r, 8) r> 0 r<0 (r, 0) = (r, 8) = X X X x x Warrow_forward
- 74. Geometry of implicit differentiation Suppose x and y are related 0. Interpret the solution of this equa- by the equation F(x, y) = tion as the set of points (x, y) that lie on the intersection of the F(x, y) with the xy-plane (z = 0). surface Z = a. Make a sketch of a surface and its intersection with the xy-plane. Give a geometric interpretation of the result that dy dx = Fx F χ y b. Explain geometrically what happens at points where F = 0. yarrow_forwardExample 3.2. Solve the following boundary value problem by ADM (Adomian decomposition) method with the boundary conditions მი მი z- = 2x²+3 дг Əz w(x, 0) = x² - 3x, θω (x, 0) = i(2x+3). ayarrow_forward6. A particle moves according to a law of motion s(t) = t3-12t2 + 36t, where t is measured in seconds and s is in feet. (a) What is the velocity at time t? (b) What is the velocity after 3 s? (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (e) What is the acceleration at time t? (f) What is the acceleration after 3 s?arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning





