Convergence of three series with alternating and trigonometric terms

[ellaingeborg]

Homework Statement

Determine whether the following series converge, converge conditionally, or converge absolutely.

Homework Equations

a) Σ(-1)^k×k^3×(5+k)^-2k (where k goes from 1 to infinity)

b) ∑sin(2π + kπ)/√k × ln(k) (where k goes from 2 to infinity)

c) ∑k×sin(1+k^3)/(k + ln(k)) (where k goes from 1 to infinity)

The Attempt at a Solution

I tried using the integral test and the alternating series test, but couldn't figure it out. Any help is appreciated, thank you.

 

[tnich]

Homework Statement

Determine whether the following series converge, converge conditionally, or converge absolutely.

Homework Equations

a) Σ(-1)^k×k^3×(5+k)^-2k (where k goes from 1 to infinity)

b) ∑sin(2π + kπ)/√k × ln(k) (where k goes from 2 to infinity)

c) ∑k×sin(1+k^3)/(k + ln(k)) (where k goes from 1 to infinity)

The Attempt at a Solution

I tried using the integral test and the alternating series test, but couldn't figure it out. Any help is appreciated, thank you.

It's difficult to help you if you don't show us what you have tried. Let's start with part a). Show us how you would apply the alternating series test to it.

 

[Ray Vickson]

It's difficult to help you if you don't show us what you have tried. Let's start with part a). Show us how you would apply the alternating series test to it.

More to the point: it is a violation of PF rules for us to offer help if the OP has not shown the work done.

 

[Mark44]

@ellaingeborg, please pick one of the three problems and show us what you have tried.
All others, please refrain from posting until we hear back from the OP.