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Show that (1 x 2^2 + 2 x 3^2+....+nx(n+1)^2)/(1^2 x 2+ 2^3 x 3+....+n^2(n+1))=(3n+5)/(3n+1)

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Show that (1 x 22 + 2 x 32+....+nx(n+1)2)/(12 x 2+ 23 x 3+....+n2(n+1))=(3n+5)/(3n+1)

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nth term of the numerator = n(n + 1)2 = n3 + 2n2 + n

nth term of the denominator = n2(n + 1) = n3 + n2  

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