The Tower Of Fractions

Algebra Level 4

\[ \large \frac { \frac { \frac { \frac { \frac { \frac { \frac { \frac { \frac { 9 }{ 8 } }{ 7 } }{ 6 } }{ 5 } }{ 4 } }{ 3 } }{ 2 } }{ 1 } }{ \frac { 2 }{ \frac { 3 }{ \frac { 4 }{ \frac { 5 }{ \frac { 6 }{ \frac { 7 }{ \frac { 8 }{ 9 } } } } } } } } =\dfrac { A }{ B } \]

Given that \(A\) and \(B\) are positive and coprime integers.

Find \(A+B\).

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