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 <math>\frac{n(n+1)+n(n-1)}{2}</math>. Then Multiply: <math>\frac{n^2+n+n^2-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 <math>\frac{n(n+1)+n(n-1)}{2}</math>. Then Multiply: <math>\frac{n^2+n+n^2-n}{2}</math>. Finnaly the <math>n</math>'s in the numorator cancel leaving us with $\frac{n^2+n^2}{2}=n^2 |
Revision as of 13:34, 14 June 2019
Here are many proofs for the Theory that 
PROOF 1: , Hence 
. If you dont get that go to Proof without words. If you conbine the fractions you get 
. Then Multiply: 
. Finnaly the 
's in the numorator cancel leaving us with $\frac{n^2+n^2}{2}=n^2
