Question 6 (20 points). Determine whether the following series converge or diverge, and by which test: o arctan(k) k-0 oo ok k! k-0 Question 6 (20 points). Determine whether the following series...
(a) Determine whether the series converge absolutely, converge conditionally or diverge k 2 (2 + k3) (k!)3 (3k)! cos kT In k k= 1 k-1 (a) Determine whether the series converge absolutely, converge conditionally or diverge k 2 (2 + k3) (k!)3 (3k)! cos kT In k k= 1 k-1
4. Use the integral test to determine whether the following series converge or diverge. Hint: Use a u-substitution for each integral. n=2 B. nln (n) .nInnInI(n) 4. Use the integral test to determine whether the following series converge or diverge. Hint: Use a u-substitution for each integral. n=2 B. nln (n) .nInnInI(n)
Determine whether the following series converge or diverge.
Determine if the following series converge or diverge by using the appropriate test. 8. 7* Determine if the following series converge or diverge by using the appropriate test. 8. 7*
(1) Determine whether the following series converge or diverge: (a) - ke-k2 (b) k=1 n2+39 1 (c) } + 4 + 1 + i +.
Determine whether the series Grange or duerge Determine whether the salles Converge or diverge
Use the ratio test to find whether the following series converge or diverge 7 Yl
3. If the series 2-1 bn is converge, determine whether the series - converge or diverge! 4. A right triangle ABC with the angle at A is and the length of the side |AC|=b. The side CD, EF, FG, etc is perpendicular to AB, while DE, FG, etc is perpendicular to BC as shown below: G E с As you can see the length 1CD to DE, to IEF, to |FG|, etc is getting smaller and smaller. Using the picture...
3. If the series 2-1 bn is converge, determine whether the series - converge or diverge! 4. A right triangle ABC with the angle at A is and the length of the side |AC|=b. The side CD, EF, FG, etc is perpendicular to AB, while DE, FG, etc is perpendicular to BC as shown below: G E с As you can see the length 1CD to DE, to IEF, to |FG|, etc is getting smaller and smaller. Using the picture...
3. Use the Leibniz test (alternating series test) to test whether the power series for arctan(x) centered at 0 converges for the end points as well Bonus: Assuming the series you found for arctan(x) is stil a valid formula at the endpoints, find a series formula for T that only has rational terms (each term is a fraction of integers) 3. Use the Leibniz test (alternating series test) to test whether the power series for arctan(x) centered at 0 converges...