Can anyone please check/confirm my work on this proof?

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The proof submitted for review is incorrect due to an error in the final equation, which does not align with the formula for n+1. Additionally, the proof attempts to establish the wrong series, as it should focus on 12 + 22 + ... + n² rather than 1 + 2 + ... + n. The feedback highlights the need for clarity in the proof's objective and accuracy in calculations. Overall, the reviewer emphasizes the importance of addressing these fundamental issues for a valid proof. The discussion underscores the necessity of precise mathematical reasoning in proofs.
Math100
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Homework Statement
Prove 1^2+2^2+...+n^2=(1/6)n(n+1)(2n+1) for all positive integers n.
Relevant Equations
None.
Please check/confirm my work of this proof and tell me if it's correct or not. Thank you.
 

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Your proof is not correct. Your final equation is not equal to the formula for n+1, and you are trying to prove the wrong thing anyway. The series is 12 + 22 +...+ n2, not 1 + 2 +...+n.
 
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