6. Given that P(n) is the equation 1· (1!) +2 · (2!) + ...+n· (n!) = (n+1)! – 1, where n is an integer such that n > 1, we will prove that P(n) is true for all n >1 by induction. (a) Base case: i. Write P(1). ii. Show that P(1) is true. In this case, this requires showing that a left-hand side is equal to a right-hand side. (b) Inductive hypothesis: Let k > 1 be a natural number. Assume P(k) is true. Write P(k). (c) Inductive step: i. Write P(k + 1). ii. Use the assumption that P(k) is true to prove that P(k+ 1) is true.
6. Given that P(n) is the equation 1· (1!) +2 · (2!) + ...+n· (n!) = (n+1)! – 1, where n is an integer such that n > 1, we will prove that P(n) is true for all n >1 by induction. (a) Base case: i. Write P(1). ii. Show that P(1) is true. In this case, this requires showing that a left-hand side is equal to a right-hand side. (b) Inductive hypothesis: Let k > 1 be a natural number. Assume P(k) is true. Write P(k). (c) Inductive step: i. Write P(k + 1). ii. Use the assumption that P(k) is true to prove that P(k+ 1) is true.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Given that P(n) is the equation 1. (1!) + 2 · (2!) + · · · + n ·
an integer such that n > 1, we will prove that P(n) is true for all n > 1 by induction.
6.
(п!) — (п + 1)! — 1, where n is
(а) Base case:
i. Write P(1).
ii. Show that P(1) is true. In this case, this requires showing that a left-hand side is equal to a
right-hand side.
(b) Inductive hypothesis: Let k > 1 be a natural number. Assume P(k) is true. Write P(k).
(c) Inductive step:
i. Write P(k + 1).
ii. Use the assumption that P(k) is true to prove that P(k +1) is true.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad281aeb-79af-4eda-b9b4-346ba477171b%2Fd9f348ba-e8fe-4d85-8695-52e1d8a378c2%2Fnt83bt_processed.png&w=3840&q=75)
Transcribed Image Text:Given that P(n) is the equation 1. (1!) + 2 · (2!) + · · · + n ·
an integer such that n > 1, we will prove that P(n) is true for all n > 1 by induction.
6.
(п!) — (п + 1)! — 1, where n is
(а) Base case:
i. Write P(1).
ii. Show that P(1) is true. In this case, this requires showing that a left-hand side is equal to a
right-hand side.
(b) Inductive hypothesis: Let k > 1 be a natural number. Assume P(k) is true. Write P(k).
(c) Inductive step:
i. Write P(k + 1).
ii. Use the assumption that P(k) is true to prove that P(k +1) is true.
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