7. (20 points) Prove by induction that, for every positive integer n, we have n· (5n + 11) (3 + 5i) i=1
7. (20 points) Prove by induction that, for every positive integer n, we have n· (5n + 11) (3 + 5i) i=1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![**Problem 7.** (20 points) Prove **by induction** that, for every positive integer \( n \), we have
\[
\sum_{i=1}^{n} (3 + 5i) = \frac{n \cdot (5n + 11)}{2}
\]
**Problem 8. Extra credit.** (10 points) Let \( A, B, \) and \( C \) be three sets, and let \( f : A \rightarrow B \) and \( g : B \rightarrow C \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6550f6f6-7442-466d-86f7-12e7dd1263c9%2F2ff2b8f6-7880-49a2-9558-db99e0ed569d%2F8nj6j2f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 7.** (20 points) Prove **by induction** that, for every positive integer \( n \), we have
\[
\sum_{i=1}^{n} (3 + 5i) = \frac{n \cdot (5n + 11)}{2}
\]
**Problem 8. Extra credit.** (10 points) Let \( A, B, \) and \( C \) be three sets, and let \( f : A \rightarrow B \) and \( g : B \rightarrow C \)
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