**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 **

Note: The main program, SERIES, will
call a subprogram, SIGMA. All programs are given below.

<< "X" ":X:" INPUT | |

OBJ'X' STO | |

"N" ":N:" INPUT | |

OBJ'N' STO | |

0 'K' STO 0 'S' STO | |

SIGMA S "SERIES"TAG | |

F EVAL "F(X)"TAG | |

{X N K S} PURGE>> | |

ENTER 'SERIES' STO | {This stores the program under variable name SERIES.} |

<<0 N FOR C FUNC EVAL | |

S + 'S' STO K 1 + 'K' STO | |

NEXT>> | |

ENTER 'SIGMA' STO | {This stores the program under the variable name SIGMA} |

**Running the Program**

You will need to enter an expression and the corresponding
function into the variables FUNC and F, respectively. Follow the instructions
in Intro to Programming if you have not
done this before.

To test the program try the following:

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

Your answer will be

Series Value

1.6458333333

F(X) Value

1.6487212707