How do I approach this question?
How do I approach this question? 73. + a) Show that the series 1 + +...
1. A series has the property that lim an = 0. Which of the following is true? (a) The series converges and has the sum 0. (b) The series is convergent but its sum is not necessarily 0. (c) The series is divergent. (a) There is not enough information to determine whether the series converges or diverges. 1 n-00 2 2. A sequence {sn} of partial sums of the series an has the property that lim sn Which of the...
Please answer all parts. (1 point) Series: A Series (Or Infinite Series) is obtained from a sequence by adding the terms of the sequence. Another sequence associated with the series is the sequence of partial sums. A series converges if its sequence of partial sums converges. The sum of the series is the limit of the sequence of partial sums For example, consider the geometric series defined by the sequence Then the n-th partial sum Sn is given by tl...
How do I approach this Q? 1 1 1 + + (1) co 4 1 1 1 1 1 1 *82. (To illustrate that a conditionally convergent series, when rearranged, can have a different sum.) Consider 1- 2 and (2) 2 4 3 8 5 10 12 Check that (1) is conditionally convergent with limit S say, and that the terms in (2) are just a rear- rangement of those of (1). Denote the sum of the first n terms...
please show all work Determine whether the following series converges or diverges. 15 (3n - 1)(3n+2) + n=1 O A. This is a p-series with p = Sinceps the series diverges. 9 OB. The limit of the terms of the series is By the Divergence Test, the series converges. O C. This is a p-series with p = Since p> the series converges. 1 O D. This is a telescoping series and lim Sn Therefore, the series diverges. n0 O...
2. Prove that the infinite series Ex=1(-1)k diverges. (Hint: Compute the first few terms of the sequence of partial sums and determine a formula for the nth partial sum, Sn. Using this, give a formal proof, starting with the definition for divergence of this series. (Additional reference: Workshop Week #7)
(1 point) Each of the following statements is an attempt to show that a given series is convergent or divergent using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (for "correct") if the argument is valid, or enter 1 (for "incorrect") if any part of the argument is flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you must enter I.) < 2-3 1. For all n >...
1. A series Can has the property that lim on = 0. Which of the following is true? (a) The series converges and has the sum 0. (b) The series is convergent but its sum is not necessarily 0. (c) The series is divergent. (d) There is not enough information to determine whether the series converges or diverges. 2. A sequence { $m} of partial sums of the series an has the property that lims Which of the following is...
Please show how Option A- 39999 is the correct answer. n+1 Given that the series is convergent, find a value of n for which the nth partial sum is vn n-1 guaranteed to approximate the sum of the series to two decimal places O (5 pts)39,999 X (0pts) 3,999 O (0pts) 399 O (0pts) 39 n+1 Given that the series is convergent, find a value of n for which the nth partial sum is vn n-1 guaranteed to approximate the...
True of False (g) does the power series from ∞ to n=1 (x−2)^n /n(−3)^n has a radius of convergence of 3. (h) If the terms an approach zero as n increases, then the series an converges? (i) If an diverges and bn diverges, then (an + bn) diverges. (j) A power series always converges at at least one point. (l) The series from ∞ to n=1 2^ (−1)^n converges?
i 10 (1 point) Consider the series -. Let s, be the n-th partial sum; that is, in +9 10 Sn = i +9 Find 84 and so S4 S8 =