Can you find its general term?

Algebra Level 4

n=120n2+1n2+n2n\sum_{n=1}^{20} \frac{n^2+1}{n^2+n}\cdot2^n The value of the summation above can be expressed as ab223,\frac{a}{b}\cdot2^{23}, where aa and bb are coprime positive integers. Find the value of a+b.a+b.

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