11. Consider the following infinite series. Complete parts (a) through (c). 30(0.1)K k =1 a. Find the first four partial sums Sy, $2, S3, and $4- S1 = S2 = S3 = SA= (Simplify your answer. Type integers or decimals.) b. Find a formula for the nth partial sum S, of the infinite series. Sn = (Use integers or fractions for any numbers in the expression.) Use the formula to find the next four partial sums S. S, Sy, and S of the infinite series. Ss = S6 = S7 = S8 = (Simplify your answer. Type integers or decimals.) c. Make a conjecture for the value of the series. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The value of the infinite series is (Type an integer or a simplified fraction.) O B. The infinite series diverges.8. Consider the following recurrence relation. Using a calculator, make a table with at least 10 terms and determine a plausible value for the limit of the sequence or state that it does not exist. an+1 = 2an + 9; ap = 4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The plausible value for the limit of the sequence is (Type an integer or decimal rounded to three decimal places as needed.) O B. The sequence diverges. 9. Suppose a ball is thrown upward to a height of ho meters. After each bounce, the ball rebounds to a fraction r of its previous height. Let h, be the height after the nth bounce. Consider the following values of ho and r. Complete parts (a) and (b) below. ho = 50, r= 0.25 (a) Find the first four terms of the sequence of heights {h }- my = [ 7ng = [ (Type integers or decimals rounded to three decimal places as needed.) (b) Find an explicit formula for the nth term of the sequence {hr}. (Type your answer using exponential notation.) 10. For the following infinite series, find the first four terms of the sequence of partial sums. Then make a conjecture about the value of the infinite series or state that the series diverges. 0.7 + 0.07 +0.007 + ... What are the first four terms of the sequence of partial sums? S1 = $2 = | S3 = SA = (Type integers or decimals rounded to four decimal places as needed.) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The value of the infinite series is (Type an integer or a simplified fraction.) O B. The infinite series diverges