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The sum of some even numbers starting from 2 is 420. Find the number of even numbers added. |
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Answer» 2 + 4 + 6 + .... + 2n = 420 2(1 + 2 + 3 + .... + n) = 420 \(2\times\frac{n(n+1)}{2}=420\) \(n^{2}+n+(\frac{1}{2})^{2}=420+(\frac{1}{2})^{2}\) \((n+\frac{1}{2})^2=\frac{1681}{4}=(\frac{41}{2})^2\) \(n+\frac{1}{2}=\frac{41}{2}\) n = 20 Sum of 20 even numbers is 420. |
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