Can you find its general term?

Algebra Level 4

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

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