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Special “Series” (Part 1)

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Presentation on theme: "Special “Series” (Part 1)"— Presentation transcript:

1 Special “Series” (Part 1)
Dr. Shildneck

2 Nested Radicals A nested radical expression is a radical in which the sum of a pattern of radicals are “nested” continually under the previous radical. An infinite nested radical is a nested radical that continues the pattern forever. Examples of infinite nested radicals: … … … …

3 Evaluating Infinite Nested Radicals
The Procedure Set the expression equal to x Get the radical part by itself Square both sides Replace the infinite part (that looks exactly like what you started with) of the result with x Solve the resulting quadratic equation Eliminate the “impossible” solution [Example 1] …

4 Evaluating Infinite Nested Radicals
The Procedure Set the expression equal to x Get the radical part by itself Square both sides Replace the infinite part (that looks exactly like what you started with) of the result with x Solve the resulting quadratic equation Eliminate the “impossible” solution [Example 2] …

5 Evaluating Infinite Nested Radicals
The Procedure Set the expression equal to x Get the radical part by itself Square both sides Replace the infinite part (that looks exactly like what you started with) of the result with x Solve the resulting quadratic equation Eliminate the “impossible” solution [Example 3] …

6 Continued Fractions A continued fraction is a real number that is expressed in the form: where a0, a1, a2, … and b1, b2, b3, … are integers.

7 Evaluating Continued Fractions
The Procedure Set the expression equal to x Get the fractional part by itself Replace the infinite part (that looks exactly like what you started with that is inside the fraction) with x Solve the resulting equation Eliminate the “impossible” solution [Example 4]

8 Evaluating Continued Fractions
The Procedure Set the expression equal to x Get the fractional part by itself Replace the infinite part (that looks exactly like what you started with that is inside the fraction) with x Solve the resulting equation Eliminate the “impossible” solution [Example 5]

9 Assignment Special Series Worksheet 1

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