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5. Give a summation-free formula for the ordinary and exponential generating functions for each sequence. (a) an = (-1)". (This sequence alternates 1, −1, 1, −1, … …..) (b) bn = n. (This sequence begins 0, 1, 2, 3,... and continues on forever. For both functions, you may want to factor an x out of the infinite sum.)

5. Give a summation-free formula for the ordinary and exponential generating functions for each sequence. (a) an = (-1)". (This sequence alternates 1, −1, 1, −1, … …..) (b) bn = n. (This sequence begins 0, 1, 2, 3,... and continues on forever. For both functions, you may want to factor an x out of the infinite sum.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 71E
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5. Give a summation-free formula for the ordinary and exponential generating functions for each sequence. (a) an = (-1)". (This sequence alternates 1, −1, 1, −1, … …..) (b) bn = n. (This sequence begins 0, 1, 2, 3,... and continues on forever. For both functions, you may want to factor an x out of the infinite sum.)
Transcribed Image Text:5. Give a summation-free formula for the ordinary and exponential generating functions for each sequence. (a) an = (-1)". (This sequence alternates 1, −1, 1, −1, … …..) (b) bn = n. (This sequence begins 0, 1, 2, 3,... and continues on forever. For both functions, you may want to factor an x out of the infinite sum.)
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