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Find the sum of the numbers in the $n^{th}$ set: $(1)$, $(2,3)$, $(4,5,6)$, $(7,8,9,10)$.....

$(a)\;\large\frac{n(n^2+2)}{2}\qquad(b)\;\large\frac{n^2(n+1)}{2}\qquad(c)\;\large\frac{n(n^2+1)}{2}\qquad(d)\;None\;of\;these$

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