- #1

Amaelle

- 310

- 54

- Homework Statement
- Show that the following sequence is convergent

- Relevant Equations
- Racine test

Good day

I have a question about the convergence of the following serie

I understand that the racine test shows that it an goes to 2/3 which makes it convergent

but I also know that for a sequence to be convergent the term an should goes to 0 but the lim(n---->inf) ((2n+100)/(3n+1))^n)=lim exp(n*log(2n+100)/(3n+1))=+infinity

I'm really confused

thank you!

I have a question about the convergence of the following serie

I understand that the racine test shows that it an goes to 2/3 which makes it convergent

but I also know that for a sequence to be convergent the term an should goes to 0 but the lim(n---->inf) ((2n+100)/(3n+1))^n)=lim exp(n*log(2n+100)/(3n+1))=+infinity

I'm really confused

thank you!