Prove that e is an irrational number using the following argument by contradiction. Suppose that e...
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Prove that e is an irrational number using the following argument by contradiction. Suppose that e = M/N, where M, N are nonzero integers. (a) Show that M!e-¹ is a whole number. (b) Use the power series for e* at x = -1 to show that there is an integer B such that M!e-¹ equals 1 1 (M + 1)(M + 2) B + (-1)M+1 ¹ (M²+₁` - ....) + ... (c) Use your knowledge of alternating series with decreasing terms to conclude that 0 Prove that e is an irrational number using the following argument by contradiction. Suppose that e = M/N, where M, N are nonzero integers. (a) Show that M!e-¹ is a whole number. (b) Use the power series for e* at x = -1 to show that there is an integer B such that M!e-¹ equals 1 1 (M + 1)(M + 2) B + (-1)M+1 ¹ (M²+₁` - ....) + ... (c) Use your knowledge of alternating series with decreasing terms to conclude that 0
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Related Book For
Introduction to Real Analysis
ISBN: 978-0471433316
4th edition
Authors: Robert G. Bartle, Donald R. Sherbert
Posted Date:
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