Examine the sum of the first n positive integers, E1 (2i – 1) = 1+3+5+...+(2n – 1) i=1 Provide a proof that this sum has the explicit formula of n^2. That is, prove that Vn e Z+, P(n): E (2i – 1) = n? =D1 Requirements: -Identify the basis step, the inductive step, and if any assumptions, deductions, and conclusions -Proof must include a mathematical statement on the with its justification on the right as such below

Linear Algebra: A Modern Introduction
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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Examine the sum of the first n positive integers,
E1 (2i – 1) =1+3+5+...+(2n – 1)
Provide a proof that this sum has the explicit formula of n^2. That is, prove that
VnE Zt, P(n): EL (2i — 1) — п?
=D1
Requirements:
-Identify the basis step, the inductive step, and if any assumptions, deductions,
and conclusions
-Proof must include a mathematical statement on the with its justification on the
right as such below
Statement
Justification
Transcribed Image Text:Examine the sum of the first n positive integers, E1 (2i – 1) =1+3+5+...+(2n – 1) Provide a proof that this sum has the explicit formula of n^2. That is, prove that VnE Zt, P(n): EL (2i — 1) — п? =D1 Requirements: -Identify the basis step, the inductive step, and if any assumptions, deductions, and conclusions -Proof must include a mathematical statement on the with its justification on the right as such below Statement Justification
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