Summation

Algebra Level 5

i=120i5+i3i4+i2+1=15+1314+12+1+25+2324+22+1+35+3334+32+1+45+4344+42+1+...\sum_{i=1}^{20} \frac{ i^5 + i^3} { i^4 + i^2 + 1 } = \dfrac{1^5 + 1^3}{1^{4} + 1^{2} + 1} + \dfrac{2^5 + 2^3}{2^{4} + 2^{2} + 1} + \dfrac{3^5+3^3}{3^{4} + 3^{2} + 1} + \dfrac{4^5+4^3}{4^{4} + 4^{2} + 1} +...

The above 20 term summation can be expressed as AB\frac{A}{B}, for A,B A, B are coprime integers. Find A+B A + B.

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