Factorial Sum

Algebra Level 3

3!+4!2(1!+2!)+4!+5!3(2!+3!)++102!+103!101(100!+101!)= ?\frac{3!+4!}{2(1!+2!)}+\frac{4!+5!}{3(2!+3!)}+\ldots+\frac{102!+103!}{101(100!+101!)} = \ ?

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