Questions from Calculus

Q: Use the comparison test to determine whether the infinite series is convergent

Use the comparison test to determine whether the infinite series is convergent or divergent. ∑k=1∞ 1/5k cos2 (kπ/4) [Compare with ∑k=1∞ 1/5k.]

Q: Use the comparison test to determine whether the infinite series is convergent

Use the comparison test to determine whether the infinite series is convergent or divergent. ∑k=0∞ 1/(3/4)k + (5/4)k [Compare with ∑k=0∞ (3/4)-k or ∑k=0∞ (5/4)-k.]

Q: Can the comparison test be used with ∑k=2∞

Can the comparison test be used with ∑k=2∞ 1/(k ln k) and ∑k=2∞ 1/k to deduce anything about the first series?

Q: Can the comparison test be used with a ∑k=1

Can the comparison test be used with a ∑k=1∞ 1/(k2 ln k) and ∑k=2∞ 1/k2 to deduce anything about the first series?

Q: The following property is true for any two series (with possibly

The following property is true for any two series (with possibly some negative terms): Let ∑k=1∞ ak and ∑k=1∞ bk be convergent series whose sums are S and T, respectively. Then, ∑k=1∞ (ak + bk) is a c...

Q: Let ∑k=1∞ ak be a convergent series with

Let ∑k=1∞ ak be a convergent series with sum S, and let c be a constant. Then, ∑k=2∞ cak is a convergent series whose sum is c * S. Make a geometric picture to illustrate why this is true when c = 2 a...

Q: Use Exercise 29 to show that the series ∑k=0

Use Exercise 29 to show that the series ∑k=0∞ (8k + 9k)/10k is convergent, and determine its sum. Exercise 29: The following property is true for any two series (with possibly some negative terms): L...

Q: Use Exercise 30 to show that the series ∑k=1

Use Exercise 30 to show that the series ∑k=1∞ 3/k2 is convergent. Then, use the comparison test to show that the series ∑k=1∞ e1/k/k2 is convergent. Exercise 30: Let ∑k=1∞ ak be a convergent series w...

Q: Determine the third and fourth Taylor polynomials of cos x at x

Determine the third and fourth Taylor polynomials of cos x at x = π.

Q: Use the integral test to determine whether the infinite series is convergent

Use the integral test to determine whether the infinite series is convergent or divergent. (You may assume that the hypotheses of the integral test are satisfied.) ∑k=1∞ 3/√k