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!e¹ 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!e¹ 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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Introduction to Real Analysis
ISBN: 9780471433316
4th edition
Authors: Robert G. Bartle, Donald R. Sherbert
Posted Date:
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