Convergence of the order

[stefanvr]

examine the convergence of the order depending on the real parameters p and q , ([MATH]p,q\in R[/MATH])
[MATH]\\\Sigma_{n=1}^\infty (-p)^n\frac{(2n+3)^q}{2n+1}[/MATH]

 

[Deleted member 4993]

examine the convergence of the order depending on the real parameters p and q , ([MATH]p,q\in R[/MATH])
[MATH]\\\Sigma_{n=1}^\infty (-p)^n\frac{(2n+3)^q}{2n+1}[/MATH]

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

examine the convergence of the order depending on the real parameters p and q , ([MATH]p,q\in R[/MATH])
[MATH]\\\Sigma_{n=1}^\infty (-p)^n\frac{(2n+3)^q}{2n+1}[/MATH]

 

[HallsofIvy]

I believe you mean "order of convergence" rather than "convergence of the order". That is, how fast the sum converges to its limit.

 

[stefanvr]

Should I use another criterion of convergence maybe?