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.
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.
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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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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