Supplementary Problems, from section 10.3 (10 points) 1.) Show that the following series are convergent and...
answer the following questions a) Explain and show why the series k’ – 5 1, 2 21,17 is divergent. k=2 b) Determine whether the series S=272,7 is convergent or divergent by expressing the partial series, Sn , as a telescoping sum. If it is convergent, find the sum. k=
3. 45 Determine whether each of the following series is convergent or divergent by either finding a formula for its n th partial sum or using the Divergence Test. If the series is convergent, find its sum - ) (Hint: (e) 4+ (f) 31-5"/2 16 . + 25 32 125 m=1 2 n=1 n2+4n+3 (g) 3. 45 Determine whether each of the following series is convergent or divergent by either finding a formula for its n th partial sum or...
1. Use the Limit Comparison Test to prove that the series S(a, b) converges unless a or b is a negative integer. Why must this restriction on a and b be imposed? 2. In all that follows we assume without losing generality that a >b. Use partial fractions to show that 3. To get warmed up, write the first few terms of the series S(1,0) k(k + I )-4 k--J . Write the nth term of the sequence of partial...
Consider the following series and if convergent, find their sums: a.) b.) n=1 to ∞ 24/n(n+3) c.) We were unable to transcribe this imageDetermine whether the series is convergent 3 m243) O convergent O divergent If it is convergent, find its sum. (If the quant 5. -/4 POINTS SCALCCC4 8.2.034. Consider the following series. (n+1) (a) Determine whether the series is converge O convergent divergent (b) If it is convergent, find its sum. (Otherwise 50. 3 Calendar Calculus II: Homework 3A......
10. [1/9 Points] DETAILS PREVIOUS ANSWERS SCALCET8 11.2.041. Determine whether the series is convergent or divergent. 00 8 + n(n + 1) n = 1 convergent divergent If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.) 8.6558 X
Q2 (Show your work!) 16 Points Determine whether each of the given series is absolutely convergent, conditionally convergent or divergent. Q2.1 8 Points I am, where an = (+3)x=1 n=1 Please select file(s) Select file(s) Save Answer Q2.2 8 Points Q 3n2 - n +1 5n5 +n + 2 n=1 Please select file(s) Select file(s) Save Answer
Q2 (6 points) Determine whether the following series is absolutely convergent, conditionally convergent, or divergent. (-1)" 2 2n2+1 • State the name of the correct test(s) that you used to reach the correct conclusion. • Show all work. • State your conclusion. + Drag and drop your files or click to browse...
Consider the following alternating series. (-1)*+ 1 3k k=1 (a) Show that the series satisfies the conditions of the Alternating Series Test. 1 3" Since lim o and an + 1 for all n, the series is convergent (b) How many terms must be added so the error in using the sum S, of the first n terms as an approximation to the sum n=10 X (c) Approximate the sum of the series so that the error is less than...
Show all of your work and leave your answers in exact form. For exercises 1 and 2, calculate the first five terms of the sequence of partial sums correct to four decimal places. Does it appear that the series is convergent? (Just make a guess, not proof is necessary. Exercise 1: p. 755,5. Σ Exercise Σοοί(-1)"-1 2. For exercises 3 and 4, determine whether the series is convergent or divergent (make sure to state any theorems that you use). If...
Consider the series following series of functions ' sin(nx) 3 n-1 a) Show that the series is absolutely and uniformly convergent on the real axis. Let f be its summation function n sin(nx) b) Show that f E C(R) and that 1 cos(nx) f'(x)= 2-1 c) Show that 「 f#072821) f(x)dx = k=0 Consider the series following series of functions ' sin(nx) 3 n-1 a) Show that the series is absolutely and uniformly convergent on the real axis. Let f...