Question 2. Use induction to show that for any natural n ≥ 3, one can be written as a sum of n 1 distinct fractions of the form where k is a natural number.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 91E
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Question 2. Use induction to show that for any natural n ≥ 3, one can be written as a sum of n
1
distinct fractions of the form
1
Example. For n = 3, 1 = +
2 3
1
116
b+1
Hint. Note that
+
where k is a natural number.
4 1
+
1
b(b + 1)*
This is useful for the induction step.
Transcribed Image Text:Question 2. Use induction to show that for any natural n ≥ 3, one can be written as a sum of n 1 distinct fractions of the form 1 Example. For n = 3, 1 = + 2 3 1 116 b+1 Hint. Note that + where k is a natural number. 4 1 + 1 b(b + 1)* This is useful for the induction step.
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