Prove that e is an irrational number using the following argument by contradiction. Suppose that e = M/N, where M, N are nonzero integers.
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- 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- equals 1 1 (M + 1)(M + 2) B + (-1)M+1 (M+` - ....) + ... (c) Use your knowledge of alternating series with decreasing terms to conclude that 0
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Introduction to Real Analysis
Authors: Robert G. Bartle, Donald R. Sherbert
4th edition
471433314, 978-1118135853, 1118135857, 978-1118135860, 1118135865, 978-0471433316
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