Difference between revisions of "Sums and Perfect Sqares"

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Here are many proofs for the Theory that <math>1+2+3+...+n+1+2+3...+(n-1)=n^2</math>
 
Here are many proofs for the Theory that <math>1+2+3+...+n+1+2+3...+(n-1)=n^2</math>
  
PROOF 1: <math>1+2+3+...+n+1+2+3...+(n-1)=n^2</math>, Hence <math>\frac{n(n+1)}{2}+\frac{n(n+1)}{2}=n^2</math>. If you dont get that go to ''Proof without words''. If you conbine the fractions you get \frac{n(n+1)+n(n-1)}{2}
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PROOF 1: <math>1+2+3+...+n+1+2+3...+(n-1)=n^2</math>, Hence <math>\frac{n(n+1)}{2}+\frac{n(n+1)}{2}=n^2</math>. If you dont get that go to ''Proof without words''. If you conbine the fractions you get <math>\frac{n(n+1)+n(n-1)}{2}</math>

Revision as of 12:30, 14 June 2019

Here are many proofs for the Theory that $1+2+3+...+n+1+2+3...+(n-1)=n^2$

PROOF 1: $1+2+3+...+n+1+2+3...+(n-1)=n^2$, Hence $\frac{n(n+1)}{2}+\frac{n(n+1)}{2}=n^2$. If you dont get that go to Proof without words. If you conbine the fractions you get $\frac{n(n+1)+n(n-1)}{2}$