Section 12 1) Prove that = · 2 + 1 1/²2.3 1J ~/t 1 0 in (n+1) (n+1) for all nen ·3+~+=
Section 12 1) Prove that = · 2 + 1 1/²2.3 1J ~/t 1 0 in (n+1) (n+1) for all nen ·3+~+=
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
1.1.2
![**Section 1.2**
1) Prove that
\[
\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \cdots + \frac{1}{n(n+1)} = \frac{n}{n+1}
\]
for all \( n \in \mathbb{N} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7dbb4ae4-0d65-4baa-9481-63f79be91eca%2Ffc0e224e-23db-48f0-a4a9-1e5fef207044%2F3mzexic_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Section 1.2**
1) Prove that
\[
\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \cdots + \frac{1}{n(n+1)} = \frac{n}{n+1}
\]
for all \( n \in \mathbb{N} \).
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