Monday
April 21, 2014

Homework Help: calculus

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

Consider

∑ [(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

Answer this Question

First Name:
School Subject:
Answer:

Related Questions

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 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 - 1. integral -oo, oo [(2x)/(x^2+1)^2] dx 2. integral 0, pi/2 cot(theta...
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 - I'm having trouble with a geometric series problem. Determine if the ...
calculus - determine whether the series converges of diverges the sum from k=1 ...

Search
Members