Problem 6 The Abel summation method for a series is defined as follows. Suppose we have a series, Now define a power ser

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Problem 6 The Abel Summation Method For A Series Is Defined As Follows Suppose We Have A Series Now Define A Power Ser 1 (71.58 KiB) Viewed 51 times

Problem 6 The Abel summation method for a series is defined as follows. Suppose we have a series, Now define a power series using this series: Define the Abel sum of the series to be ∞ ∞ A(x) = Σ n=0 Find the Abel sum of the divergent series Σ n=0 an ao + a₁ + a₂ + a3 + ... an xn = a + a₁x + a₂x² + a3x³ + ... S = lim A(x). x 17 1−1+1−1+1 − · · · = 1- x + x² - x³ + x² - .... This is a geometric series with initial term a = 1 and ratio r = -x. See Module Hint: Here, A(x) = 3 Part 1 for the needed formula for the sum of a geometric series.