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# Final Cal Project

### Series

Question | Answer |
---|---|

1-x+x^2-....+(-x)^n | 1/1+x |

x-x^3/3!+x^5/5!-....+(-1)^n(x^2n+1)/(2n+1)! | sin(x) |

1+x+x^2/2!+....+x^n/n! | e^x |

1+x+x^2+....+x^n | 1/1-x |

1-x^2/2!+x^4/4!-...+(-1)^n(x^2n)/(2n)! | cos(x) |

x-x^2/2+x^3/3-....+(-1)^n(x^n)/n | ln(1+x) |

f(0)+f'(0)x+f"(0)x^2/2!..... | (Power)Taylor Series generated by f at x=0 |

f(a)+f'(a)(x-a)+f"(a)(x-a)^2/2! | (Power) Taylor Series generated by f at x=a |

Sequence | a succession of numbers in order |

Series | the sum of a sequence |

Series in which each term is obtained by adding a constant to the precedin term. | Arithmetic series |

Series in which each term is obtained by multiplying the preceding term by a constant | Geometric series |

Series in which the terms alternate between positive and negative | Alternating series |

1/1+1/2+1/3+1/4+1/5+1/6+1/7.... | Harmonic series |

Series that has infinitely many terms. | Infinite series |

the sum of the first n terms of a series. | Partial sum |

An infinite series that has a limit as n approches infinity. | Convergent series |

An infinite series that has no limit as n approches infinity. | Divergent series |

An infinite Geometric series converges to? | a/(1-r) when |r|=1 |

What is an Interval of Convergence? | The interval on which the series (polynomial) represents the function. (sum) |

What is the Radius of convergence? | The radius of convergence is half the length of the interval of convergence. |

What is the center of convergence? | The midpoint of the interval of convergence. |

Does the harmonic series converge or diverge? | always diverges. |

Where does an Alternating Series converge? | Converges if 1) |a1|>|a2|>|a3| or |

Created by:
Lone_Rider