Explanation Result used: Consider the series ∑ a k with non-negative terms and r = lim k → ∞ | a k + 1 a k | . (i) If 0 ≤ r < 1 , then the series converges. (ii) If r > 1 ( including r = ∞ ) , then the series diverges. (iii) If r = 1 , then the test is inconclusive. Calculation: The given series ∑ k = 1 ∞ a k = ∑ k = 1 ∞ 2 k k ! . Here, the n th term is, a k = 2 k k ! . Thus, the ( n + 1 ) th term is, a k + 1 = 2 k + 1 ( k + 1 ) ! . Obtain the limit of | a k + 1 a k |

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter 8.5, Problem 10E

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Whether the series converges or not using the Ratio Test.

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Trolley of the overhead crane moves along the bridge rail. The trolley position is measured from the center of the bridge rail (x = 0) is given by x(t) = 0.5t^3-6t^2+19.5t-14 : 0 <= t <= 3 min. The trolley moves from point A to B in the forward direction, B to C in the reverse direction and C to D again in the forward direction. CONTROL PANEL END TRUCK- RUNWAY BEAM- BRIDGE RAIL HOIST -TROLLEY TROLLEY BUMPER TROLLEY DRIVE LPENDANT TRACK -TROLLEY CONDUCTOR TRACK WIRE ROPE -HOOK BLOCK -BRIDGE DRIVE -END TRUCK BUMPER -RUNWAY RAIL TROLLEY END STOP -CONDUCTOR BAR PENDANT FESTOONING TROLLEY FESTOONING PENDANT CABLE PENDANT x(t)=0.5t^3-6t^2+19.5t-14 v(t)=1.5t^2-12t+19.5 a(t)=(dv(t))/dt=3t-12 Fig. T2.2: The overhead crane Total masses of the trolley, hook block, and the load attached to the hook block are 110 kg, 20 kg, and 150 kg. Damping coefficient, D, is 40 kg/s. What is the total amount of energy required from the trolley motor to move the system [Hint: Use Newton's 2nd law to obtain the…

Chapter 8 Solutions

Calculus: Early Transcendentals (2nd Edition)

Ch. 8.1 - Define sequence and give an example.Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Given the series k=1k, evaluate the first four...Ch. 8.1 - The terms of a sequence of partial sums are...Ch. 8.1 - Consider the infinite series k=11k. Evaluate the...Ch. 8.1 - Explicit formulas Write the first four terms of...Ch. 8.1 - Explicit formulas Write the first four terms of...

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Whether the series converges or not using the Ratio Test.

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Whether the series converges or not using the Ratio Test.

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