+11 the sum of the squares of the first n positive integers is n^3/3+n^2/2+n/6 the sum of the cubes of the first n positive integers is n^4/4+n^3/2+n^2/4 Write an expression for the sum of the squares and cubes of the first n positive integers. Then find the sum of the first 10 squares and cubes.
+129849 n^3/3+n^2/2+n/6 = [2n^3 + 3n^2 + n]/ 6
n^4/4+n^3/2+n^2/4 = [ n^4 + 2n^3 + n^2] / 4
So.....the sum of these =
[ 4n^3 + 6n^2 + 2n + 3n^4 + 6n^3 + 3n^2 ] / 12 =
[ 3n^4 + 10n^3 + 9n^2 + 2n ] / 12
Here are the sums :
1 | 2
2 | 14
3 | 50
4 | 130
5 | 280
6 | 532
7 | 924
8 | 1500
9 | 2310
10 | 3410
