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Can anyone help me with this sum

1^10 + 2^10 + 3^10 ......... +998^10 + 999^10 + 1000^10 = ?

I read that when Gauss was a kid at school he solved the simplier problem of summing all the numbers in his head between 1 and 100, before the teacher and all the other kids, by the observing the fact that 100+1=101, 99+2= 101, 98 +3 =101, etc and that there are 50 such sums, which gives an answer of 50*101=5050 for the problem.

The above sum, with powers of 10, I heard that one of the Bernoulli brothers could solve within 10 minutes with just pen and paper.

Any ideas on how he did it? I've been trying to work out a fast way to do this sum, with integrals but am always getting stuck.

1^10 + 2^10 + 3^10 ......... +998^10 + 999^10 + 1000^10 = ?

I read that when Gauss was a kid at school he solved the simplier problem of summing all the numbers in his head between 1 and 100, before the teacher and all the other kids, by the observing the fact that 100+1=101, 99+2= 101, 98 +3 =101, etc and that there are 50 such sums, which gives an answer of 50*101=5050 for the problem.

The above sum, with powers of 10, I heard that one of the Bernoulli brothers could solve within 10 minutes with just pen and paper.

Any ideas on how he did it? I've been trying to work out a fast way to do this sum, with integrals but am always getting stuck.

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