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Choose your test Use the test of your choice to determine whether the following series converge.
56.
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Calculus: Early Transcendentals (3rd Edition)
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- Determine whether the sum of the infinite series is defined. k=115(0.3)karrow_forwardUse the formula to find the indicated partial sum of each geometric series. k=183karrow_forwardFor the series i=1510i find (a) the fourth partial sum and (b) the sum. Notice in Example 9(b) that the sum of an infinite series can be a finite numberarrow_forward
- Determine whether the sum of the infinite series is defined. 13+12+34+98+...arrow_forwardA ball has a bounce-back ratio 35 . of the height of the previous bounce. Write a series representing the total distance traveled by the ball, assuming it was initially dropped from a height of 5 feet. What is the total distance? (Hint: the total distance the ball travels on each bounce is the sum of the heights of the rise and the fall.)arrow_forwardFor the following exercises, use the geometric series k=1(12)k 28. Graph the first 7 partial sums of the series.arrow_forward
- Using the Direct Comparison Test or the Limit Comparison Test determine if the series converges or diverges.arrow_forwardWe want to use the Alternating Series Test to determine if the series: Σ (-1)+2 k=4 converges or diverges. We can conclude that: k² √5 + 19 O The Alternating Series Test does not apply because the absolute value of the terms are not decreasing. O The Alternating Series Test does not apply because the absolute value of the terms do not approach 0, and the series diverges for the same reason. O The series diverges by the Alternating Series Test. O The Alternating Series Test does not apply because the terms of the series do not alternate. O The series converges by the Alternating Series Test.arrow_forward05* Let p, q> 0. Find the relation of p and q so that the following series is convergent. p>1 and p=1,q>1 p1 p1 and p=1, q<1 8 n=1 1 n²(Inn)arrow_forward
- Find the value of x for which the given geometric series converges.Also, find the sum of the series.arrow_forwardFind the interval of convergence for the given power series. (x - 4)" Σ n(- 9)" n=1 The series is convergent from x = left end included (enter Y or N): to x = right end included (enter Y or N): M C ㅈ # $ A de L % 5 6 D 8 7 8 9 #arrow_forwardQ2arrow_forward
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