Question

sequence diverges or converges: a(sub n)=((3^n)/(4^n+1))

Answer 1

\[\frac{3^n}{4^n + 1}\]Is this it? It converges because the limit as n -> infinity is 0.

Answer 2

similar, but (n+1) is together.-- is that all u have 2 do?

Answer 3

Yeah, if it's a sequence yes. A series is more complicated, but according to MathWorld: "A sequence is said to be convergent if it approaches some limit"

Answer 4

idk, i feel series is easier.. i guess 2 much series confuse me on sequences: Wat about this sequence: an=sqrt((n^2)+5n)-(sqrt((n^2)+2n)), is is divergent because it approaches infinity?

Answer 5

It should converge again, because the limit is 3/2. (Sorry for the late response, I was calculating the limit)