# Series Examples

### Example 1

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Substitute for *n* for all whole numbers between 1 and 4. [4(1) – 1] + [4(2) – 1] + [4(3) – 1] + [4(4) – 1] [4 – 1] + [8 – 1] + [12 – 1] + [16 – 1] Multiply. 3 + 7 + 11 + 15 Subtract. 36 Add your terms to get your solution. | |

### Example 2

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Substitute for *n* for all whole numbers between 1 and 5. Find a common denominator. This is where a calculator is nice.
Add 'em up. Please remember the denominator stays the same. Please.
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### Example 3

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Rewrite the series with the constant multiple out front. Substitute for *n* for all whole numbers between 1 and 4. Simplify each term. Find a common denominator. Add in the bracket. Multiply and you are finished. If only there were an easier way to find the sum of a series that looked like this… | |

### Example 4

. Solve for *x*. | |

Start writing out terms and adding. Begin with the 0^{th} term. (0 + 3) + (1 + 3) = 3 + 4 = 7 3 + 4 + 5 = 12 3 + 4 + 5 + 6 = 18 3 + 4 + 5 + 6 + 7 = 25 Almost there... 3 + 4 + 5 + 6 + 7 + 8 = 33 Well done. 8 = *x *+ 3 Set your last term equal to your rule while subbing *x* in for *n*. 5 = *x* | |

### Example 5

Write the series using sigma notation: 2 + 4 + 6 + 8 + 10 + 12.
Rule: 2*n*
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Using 2 as the 1^{st} term, find a rule that describes all the terms. 2 = 1^{st} term so *n *= 1. 12 = 6^{th} term so *n* = 6. Decide what n should go up to. | |

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