# Break them apart

Algebra Level 2

$\large \frac { 1 }{ 2\times 3} +\frac { 1 }{ 3\times 4 } +\frac { 1 }{ 4\times 5 } +\ldots+\frac { 1 }{ 49\times 50 }$

If the expression above can be represented in the form of $\frac { a }{ b }$ ,where $\gcd (a,b)=1$, then find ${ (a+b) }^{ 3 }$.

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