Monday

December 22, 2014

December 22, 2014

Posted by **Bernie** on Saturday, August 6, 2011 at 10:58am.

∞

∑ [(3k+5)/(kČ-2k)]ᵖ, for each p ∈ ℝ.

k=3

Show this series { converges if p > 1

{ diverges if p ≤ 1

Hint: Determine the known series whose terms past the second give an approximate match for the terms of this series. This series is suitable (almost) for using the comparison test. Separate comparisons with it, or closely related series, are needed to establish convergence or divergence of the series according to p. You will need to establish inequalities, based on approximations (as below), to apply the comparison tests.

kČ - 2k ≥ kČ/2 for k ≥ 4 3k + 5 ≤ 8k

kČ > kČ - 2k k < 3k + 5

- calculus -
**Bernie**, Saturday, August 6, 2011 at 11:00amThose approximations are supposed to look like this:

kČ - 2k ≥ kČ/2 for k ≥ 4

3k + 5 ≤ 8k

kČ > kČ - 2k

k < 3k + 5

**Answer this Question**

**Related Questions**

Calculus - Find a series ∑a_n for which ∑(a_n)^2 converges but &#...

Calculus - If a_n does not equal zero for any n>=1 and ∑a_n converges ...

Calculus - Determine the following about the series. Indicate the test that was ...

calculus - determine whether the series converges of diverges the sum from k=2 ...

calculus - determine whether the series converges of diverges the sum from k=2 ...

calculus - Determine whether the given series converges or diverges, and find ...

calculus - determine whether the series converges of diverges the sum from n=1 ...

calculus - determine whether the series converges of diverges the sum from n=1 ...

calculus - 1. integral -oo, oo [(2x)/(x^2+1)^2] dx 2. integral 0, pi/2 cot(theta...

Calculus - The problem with these two questions is that I cannot determine the a...