Sunday

March 29, 2015

March 29, 2015

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

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

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

Calculus - How can I prove this series alternating series converges(this is the ...

calculus - Compute the limit of the partial sums to determine whether the series...