Program for Sin(x^2) MacLaurin Series

[Einstein2.0]

I'm currently attempting to design a program on my ti-84 calculator (ti-nspire w/ 84 faceplate) to provide an approximation of the sin(x^2) as accurate as I would like the sum the reach. I attempted to input a formula for such, sum(seq((-1)^(Z-1)*X^(4Z-2)/(2Z-1)!, Z, 1, n, 1)), "Z" being the variable of the series whose end would be determined by my input of "n", and I wanted the program to display the series INCLUDING the variable "X," hence, displaying the MacLaurin approximation of sin(x^2). I hoped to possibly graph this and use the method in some way to provide an approximate integration of sin(x^2). Could anyone let me know if this is possible or even point me in a better direction? Sorry this question has to be so long.

 

[mathman]

Start with the series for sin(y) and then let y = x². I may be missing something in your description.

 

[Einstein2.0]

Start with the series for sin(y) and then let y = x². I may be missing something in your description.

It's the fact that the calculator won't display the series w/ the variable "X" that's my real problem. I'm not really sure if the calculator can do something like that.

 

[mathman]

It's the fact that the calculator won't display the series w/ the variable "X" that's my real problem. I'm not really sure if the calculator can do something like that.

I can't help you, since I have never used a TI-84 calculator.