- #1
Saladsamurai
- 3,020
- 7
Show that [tex]\sum_{k=1}^{\infty}\frac{k+4}{k^3}[/tex] converges.
I thought I would try the limit comparison test by using [tex]a_k=\frac{k+4}{k^3}[/tex] and [tex]b_k=\frac{1}{k^3}[/tex].
I thought a_k looked similar to power series so that if the lim ask-->infinity of a_k/b_k is finite and > 0 then since the p-series (for p>1) converges, than so must a_k,
But I am getting an infinite limit.
So my questions are:
1.) Where is my reasoning flawed?
2.) What is the correct approach?
~Casey
I thought I would try the limit comparison test by using [tex]a_k=\frac{k+4}{k^3}[/tex] and [tex]b_k=\frac{1}{k^3}[/tex].
I thought a_k looked similar to power series so that if the lim ask-->infinity of a_k/b_k is finite and > 0 then since the p-series (for p>1) converges, than so must a_k,
But I am getting an infinite limit.
So my questions are:
1.) Where is my reasoning flawed?
2.) What is the correct approach?
~Casey