S.2. ∑Impares = n² - JulTob/Mathematics GitHub Wiki
1+3+5+7+9+...+m = n²
m=2n-1
function SumaImpares(n: Natural) is
m = 2·n - 1
1+3+5+7+9+...+m = n²
if n=1 then
1 = 1² = 1
is True
if s(n) then s(n+1)
1+3+5+7+9+...+m + 2(n+1)-1 = (n+1)²
n² + 2n+2 - 1 = (n+1)²
n² + 2n+2 - 1 = n²+2n+1
n² + 2n + 1 = n² + 2n + 1
is True
n = 1 ⟹ s = 1
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n = 2 ⟹ s = 4 ∆n = 3 = 2 + 1 = n + n-1 = 2n-1
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n = 3 ⟹ s = 9 ∆n = 5 = 2 + 1 = n + n-1 = 2n-1
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n = 4 ⟹ s = 16 ∆n = 7 = 4 + 3 = n + n-1 = 2n-1
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n = 5 ⟹ s = 25 ∆n = 9 = 5 + 4 = n + n-1 = 2n-1
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