**Introduction**

This program evaluates Taylor series of the form C_{K}X^{K}
or
C_{K}(X-A)^{K}.
It also compares that value to the corresponding function value, f(X).

If you have not used one of the programs posted on this website before,
you should read through
the information in the Intro to Programming
section first.

**The Program **

:Disp "X" | {Disp is in PRGM under I/O} |

:Input X | {Input is in PRGM under I/O} |

:Disp "N" | |

:Input N | |

:0K | {The 0 is a zero} {The arrow is STO } |

:0S | {The 0 is a zero} |

:Lbl 1 | {Lbl is in PRGM under CTL} |

:Y1+SS | {Y1 is in Y-VARS under FUNCTION} |

:IS>(K,N) | {IS> is in PRGM under CTL} |

:Goto 1 | {Goto is in PRGM under CTL} |

:Disp "SERIES VALUE" | {Disp is in PRGM under I/O} { " is on the + button} |

:Disp S | |

:Disp "F(X) VALUE" | |

:Disp Y2 |

**Running the Program**

You will need to enter an expression and the corresponding function f(X)
into Y1 and Y2,
respectively. The program will ask for the X value and
N (the number of terms to be evaluated).

To test the program try the following:

Enter
into Y1 and e^{x} into Y2 .
Use X = 0.5, N = 3.

Your answer will be

Series Value

1.6458333333

F(X) Value

1.6487212707