Math Problem Statement
Suppose (πͺπ) is a sequence of real numbers such that ππππββ|ππ| π/π exists and is non- zero. If the radius of convergence of the power series β πππ β π π=π is equal to π then the radius of convergence of the power series β π ππππ β π π=π is (A) less than π (B) greater than π
Solution
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Math Problem Analysis
Mathematical Concepts
Power Series
Radius of Convergence
Limits of Sequences
Formulas
Radius of convergence formula: 1/r = lim sup |cn|^(1/n)
lim nββ |n^2 cn|^(1/n) = L
Theorems
Root Test
Ratio Test
Suitable Grade Level
Undergraduate Mathematics
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