Suppose that > an = 6 and bn = -8 and a1 = -4 and b1 = -7 , use properties of series to n= 1 evaluate the following series: Given the series: a.) (-3an + 50n) = - 58 6 12 24 3+ 7 49 343 to+ ... n= 1 does this series converge or diverge? b. ) (- 3an + 5br ) = converges n =2 Enter an integer or decimal number [more.. diverges Question Help: Video @ Written Example Message instructor Submit Question If the series converges, find the sum of the series: (If the series diverges, leave this second box blank.) Question 7 0/1 pt 19-20 @ Details Score on last try: 0 of 1 pts. See Details for more. Write an explicit formula for the sequence: You can retry this question below 1 1 11 1 3' -4' 5' 6'7'-8'") Consider the series 7 an = 1 k ( k + 4 ) . If it converges, find its sum. Question Help: B Written Example Message instructor a.) First find the partial fraction decomposition of the magnitude of the kth term. Find a formula for the general term a, of the sequence assuming the pattern of the k(k + 4) continues. 6 6 6 6 6 b.) Then find the limit of the partial sums. 4' 16' 64' 256' 1024' Assume the first term is al 7 an " I k(k + 4) Enter your answer for the sum as a reduced fraction. Hint: The series is a telescoping series. Write down its terms using the partial fraction decomposition until some terms cancel. Suppose you start with one liter of vinegar and repeatedly remove 0.07L, replace with water, mix, and repeat. a. Find a formula for the concentration after n steps. 0 / 10 points b. After how many steps does the mixture contain less than 14% vinegar? Evaluate the following integral in two ways. So sin(x )In(cos(x)) da Let Sk = ) 1 a.) Evaluate using substitution. Lin! b.) Evaluate using integration by parts. Find S4. Enter exact values, not an approximation. Show all steps. Upload your work for this problem only. Question Help: Video B Written Example Message instructor 2 0/ 1 point Submit Question Evaluate the following integral with integration by p Question 5 C 0/1 pt 9 20 @ Detail: Show all steps. Upload your work to this problem only A Super Happy Fun Ball is dropped from a height of 16 feet and rebounds - of the distance from which it fell. a.) How many times will it bounce before its rebound is less than 1 foot? Enter an integer. It will bounce times before its rebound is less than 1 foot. b. ) How far will the ball travel before it comes to rest on the ground? Express your answer as an integer or reduced fraction. It will travel feet before it comes to rest on the ground. Question 12 0/1 pt 9 20 @ Details Is the given series convergent? If so, compute the sum. If not, enter DNE (does not exist) for the sum. Use exact values. (-3)" - (-2)" 7n Question Help: Video Written Example Message instructor Submit Question Question 13 0/1 pt 9 20 @ Details Express 15. 20 as a ratio of two integers