Prove that n Σ 1 n²(n + 1)² i=1 Cor all positive integers n.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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![Prove that
\[
\sum_{i=1}^{n} i^3 = \frac{1}{4} n^2 (n+1)^2
\]
for all positive integers \( n \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba208968-0ccc-4a94-8921-5ea260cefe19%2F99c748e0-c16d-4942-99b7-693c09953f06%2F3gl5sb5_processed.png&w=3840&q=75)
Transcribed Image Text:Prove that
\[
\sum_{i=1}^{n} i^3 = \frac{1}{4} n^2 (n+1)^2
\]
for all positive integers \( n \).
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