18-20. Evaluating geometric series two ways Evaluate each geomet- ric series two ways. a. Find the nth partial sum S, of the series and evaluate lim S b. Evaluate the series using Theorem 10.7. k=0 THEOREM 10.7 Geometric Series a Let a + 0 and r be real numbers. If |r| < 1, then ark If |r| > 1, k=0 then the series diverges. Diverges rs-1 Converges -1

Q: 8. Provide justification for you what will appear on the ex asked. (-1)" (2n)! (a) n=1 n4 – 4n -

A:

Q: k 1 k Consider the series Does it converge or diverge? If it k2 (k +1)2 k=2 converges, what does it…

A:

Q: 3. a) Find the limit of the sequence an = (2n²+3)(n-1) n(n² + 1)

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Consider the function 1 1- x4 Write a partial sum for the power series which represents this…

A:

Q: 2k-1 00 (9) The sum k-13k = A) 312 9/2 C) 2 D) 2/12

A:

Q: (7) A formula for the general term starting with n = 1 of: A) {} B) {} C) (-1)" 3") 472 D) 39 - ) -…

A:

Q: n² + 3 Let ak be the series whose partial sums are given by sn Find the sum of the series n(2n + 1)…

A: Consider the provided question,

Q: Which of the following statement is TRUE? (i) If Σα o an = and bn = then Στο bn n=0 2 an 3 (ii) If…

A: Solution is given below:

Q: ∞ k=1 2e-4k

A: The given series is .We have to determine whether the series is converge or diverge.

Q: ect ALL the true statements about geometric series: ar The p-series is absolutely convergent…

A: GivenA geometric series  and a p-series .Objectivea)The p-series is absolutely convergent whenever…