4.
记\(S_{k}=1^{k}+2^{k}+3^{k}+…+n^{k}\),当\(k=1\),\(2\),\(3\),\(…\)时,观察下列等式:
\({{S}_{{1}}}=\dfrac{{1}}{{2}}{{n}^{{2}}}+\dfrac{{1}}{{2}}n\),
\({{S}_{{2}}}=\dfrac{{1}}{{3}}{{n}^{3}}+\dfrac{{1}}{2}{{n}^{{2}}}+\dfrac{{1}}{{6}}n\),
\({{S}_{3}}=\dfrac{1}{4}{{n}^{4}}+\dfrac{1}{2}{{n}^{3}}+\dfrac{1}{4}{{n}^{2}}\),
\({{S}_{4}}=\dfrac{1}{5}{{n}^{5}}+\dfrac{1}{2}{{n}^{4}}+\dfrac{1}{2}{{n}^{3}}-\dfrac{1}{30}n\).
\({{S}_{5}}=A{{n}^{6}}+\dfrac{1}{2}{{n}^{5}}+\dfrac{5}{12}{{n}^{4}}+B{{n}^{2}}\),
\(……\)
由此可以推测\(A-B=\)_______.