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If $p$ = $1$ + $\large\frac{1}{2}$ + $\large\frac{1}{3}$+....+$\large\frac{1}{n}$, then $S$ = $\large\frac{1^2}{1^3}$ + $\frac{1^2+2^2}{1^3+2^3}$ + $\large\frac{1^2+2^2+3^2}{1^3+2^3+3^3}$+.... upto $n$ terms equal to

$(a)\;\frac{4}{3}\;p-1\qquad(b)\;\frac{4}{3}\;p+\frac{1}{n}\qquad(c)\;\frac{4}{3}\;p\qquad(d)\;\frac{4}{3}\;p-\frac{2}{3}\;\frac{n}{n+1}$