Answered: Suppose Sn is the following sum. 1 1 Sn…

Math

Advanced Math

Suppose Sn is the following sum. 1 1 Sn 1·2 ' n(n + 1) 2·3

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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Question

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Im supposed to find ?1,?2,?3, and ?4, and then find a guess at an explicit formula for ?n. Then I am also supposed to prove that the explicit formula for ?n is true using induction.

Suppose \( S_n \) is the following sum.

\[
S_n = \frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \cdots + \frac{1}{n(n+1)}
\]

Expert Solution

Step 1

To will find the explicit formula by using some algebraic calculations and then we prove that explicit formula using induction.

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