>>16783039

Sum[1/k^1, {k, 1, n}] = Integrate[(x^n – 1)/(x – 1), {x, 0, 1}]

Sum[1/k^2, {k, 1, n}] = Integrate[((x y)^n – 1)/(x y – 1), {x, 0, 1}, {y, 0, 1}]

Sum[1/k^3, {k, 1, n}] = Integrate[((x y z)^n – 1)/(x y z – 1), {x, 0, 1}, {y, 0, 1}, {z, 0, 1}]

Sum[1/k^4, {k, 1, n}] = Integrate[((x y z a)^n – 1)/(x y z a – 1), {x, 0, 1}, {y, 0, 1}, {z, 0, 1}, {a, 0, 1}]

et cetera