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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