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Betheny Zolt is 5' 3".

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Betheny Zolt is 5' 3".

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Maurilio De Zolt was born in 1950.

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Suppose N is a perfect number. Then N cannot be a square number and so N has an even number of factors.Suppose the factors are f(1) =1, f(2), f(3), ... , f(k-1), f(k)=N.

Furthermore f(r) * f(k+1-r) = N for r = 1, 2, ... k so that f(r) = N/f(k+1-r)

which implies that 1/f(r) = f(k+1-r)/N


Then 1/f(1) + 1/(f(2) + ... + 1/f(k)

= f(k)/N + f(k-1)/N + ... + f(1)/N

= [f(k) + f(k-1) + ... + f(1)] / N

= 2N/N since, by definition, [f(k) + f(k-1) + ... + f(1)] = 2N

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Bri Samuels is 5' 9 1/2".

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A very good try, but f(n) is still ambiguous. I assume you mean

f(n) = 1/2*n*(n+2) and not 1/[2*n*(n+2)]

Then f(n+2) - f(n) = 1/2*(n+2)*(n+2+2) - 1/2*n*(n+2)

= 1/2*(n+2)*(n+4) - 1/2*n*(n+2)

= 1/2*(n+2)*{(n + 4) - n}

= 1/2*(n+2)*4

= 2*(n+2)

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