Series Examples

Example 1

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.

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Example 2

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

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…

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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

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Example 5
Write the series using sigma notation: 2 + 4 + 6 + 8 + 10 + 12.
Rule: 2n

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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