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1^6,+1^6+2^6,+1^6+2^6+3^6,+……+1^6+2^6+3^6+…+n^6=(1/168)n(n+1)^2(n+2)(3n^4+12n^3+7n^2-10n+2)
1^5+3^5+5^5+7^5+……+(2n-1)^5=(1/3)n^2(16n^4-20n^2+7)
1*3*5*7*9+3*5*7*9*11+5*7*9*11*13+……+(2n-1)(2n+1)(2n+3)(2n+5)(2n+7)=(1/3)n(16n^5+192n^4+820n^3+1440n^2+739n-372)
1^4*2^4*3^4+2^4*3^4*4^4+3^4*4^4*5^4+…+n^4*(n+1)^4*(n+2)^4=(1/10010)n(n+1)(n+2)(n+3)(770n^9+10395n^8+55650n^7+147735n^6+195825n^5+109305n^4+13105n^3+6525n^2+2706n-1476) |
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