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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