Write out explicitly, using Bernoullis techniques, the formulas for the sums of the first n fourth, fifth, and tenth powers. Then show that the sum of the tenth powers of the first 1000 positive integers is 91, 409, 924, 241, 424, 243, 424, 241, 924, 242, and 500. Bernoulli claimed that he calculated this value in "less than half of a quarter of an hour" (without a calculator).