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you're done (as modeled in class videos); you do not need to actually do the complete proof. 1. Prove that 13 +2³+3³ +...+n³: (n(n + ¹)) ² 2 = for n € Z+

you're done (as modeled in class videos); you do not need to actually do the complete proof. 1. Prove that 13 +2³+3³ +...+n³: (n(n + ¹)) ² 2 = for n € Z+

Advanced Engineering Mathematics
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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Please answer the following question by following the instructions
**Learning Target R4 Core:** Given a statement to be proven by (weak) induction, I can state and prove the base case, state the inductive hypothesis, and outline the proof. I can describe the subtle difference between weak and strong induction. --- For each statement below, complete each of the following parts: - State and prove the base case - State the inductive hypothesis - Outline how the rest of the proof would go, that is, tell me roughly what will happen to complete the proof, identifying how this section of the proof will begin and ultimately what it will look like when you’re done (as modeled in class videos); you do not need to actually do the complete proof. 1. Prove that \(1^3 + 2^3 + 3^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2\) for \(n \in \mathbb{Z}^+\) 2. Prove that any postage greater than or equal to 23 can be made using only 5-cent and 7-cent stamps.
Transcribed Image Text:**Learning Target R4 Core:** Given a statement to be proven by (weak) induction, I can state and prove the base case, state the inductive hypothesis, and outline the proof. I can describe the subtle difference between weak and strong induction. --- For each statement below, complete each of the following parts: - State and prove the base case - State the inductive hypothesis - Outline how the rest of the proof would go, that is, tell me roughly what will happen to complete the proof, identifying how this section of the proof will begin and ultimately what it will look like when you’re done (as modeled in class videos); you do not need to actually do the complete proof. 1. Prove that \(1^3 + 2^3 + 3^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2\) for \(n \in \mathbb{Z}^+\) 2. Prove that any postage greater than or equal to 23 can be made using only 5-cent and 7-cent stamps.
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