How to calculate infinite series sums on a TI-89

[d.tran103]

Hey, I'm having trouble with plugging sum series into my Ti-89, and was wondering how to do it with things converging and going to infinity. I have the sums rounded to 3 decimal places that my professor gave me, however, I can't figure out how to get it from the calculator. For example I have,

Ʃ10(n^2)/(n^4+12)=5.960

On the worksheet it says assume each summation goes from 1 to infinity. It doesn't give me my step size, so I'm assuming it's one?

I know the command is:
sum(seq(function, variable, start, stop, step size))

and so I have:

sum(seq((10y^2)/(y^4+12),y,1,∞,1))

and it's telling me that I have a domain error.

So I tried different stops such as stuff lower than 100 and it works. So my question is how do I get the sum from 1 to infinity? Do I have to improvise and use finite stops (for example 50, etc.)? And then interpret the answer to find the real sum?

Thanks!

 

[d.tran103]

or if I do:
sum((10y^2)/(y^4+12),y,1,∞,1)

it returns
∞
10Ʃ(10y^2)/(y^4+12)
y=1

without giving me the answer (even if I hit diamond).