Convergent/Divergent Sequences

[jegues]

Homework Statement

Determine whether the sequence is convergent or divergent. Find limits for convergent sequences.

$$c_{1} = 4,$$

$$c_{n+1} = -\frac{c_{n}}{n^{2}}$$ for $$n \geq 1$$

Homework Equations

$$lim_{n\rightarrow\infty} a_{n} = L$$

Where L is a number.

The Attempt at a Solution

Okay so when n=1,

$$c_{2} = -4$$

n=2,

$$c_{3} = 1$$

n=3,

$$c_{4} = -\frac{1}{9}$$

I don't seem to be approaching a certain value here and I'm not sure how I can take the limit as n goes to infinity of the general term, because the general term itself depends on the previous term.

Any ideas?

 

[jgens]

Why don't you try looking at a few more cases before deciding that it doesn't appear to be approaching a particular value.

 

[jegues]

Why don't you try looking at a few more cases before deciding that it doesn't appear to be approaching a particular value.

Okay.

n=4,

$$c_{5} = \frac{1}{144}$$

n=5,

$$c_{5} = \frac{-1}{3600}$$

Whoops! The fact that it was flipping signs confused me, this things going to zero, whether it has a negative or not!

 

[╔(σ_σ)╝]

Yes, it goes to zero.