Math Problem Statement
Define the double factorial of π , ο»Ώdenoted π ! ! , ο»Ώas follows: π ! β { 1 * 3 * 5 c d o t s ( π
2 ) * π
π π
π
π π
o d d
2 * 4 * 6 c d o t s ( π
2 ) * π
π π
π
π π
e v e n
and (
1 ) ! β 0 ! β 1 . Find the radius of convergence for the given power series. β π
1 β 5 π * π ! * ( 4 π + 2 ) ! * ( 2 π ) ! ! 6 π * [ ( π + 3 ) ! ] 4 * ( 4 π
1 ) ! ! (
3 π₯ + 4 ) π The radius of convergence, π
Solution
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Math Problem Analysis
Mathematical Concepts
Power Series
Double Factorial
Radius of Convergence
Ratio Test
Stirling's Approximation
Formulas
Double factorial definition
Ratio test formula
Theorems
-
Suitable Grade Level
Advanced undergraduate
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