The numerator is the difference between the two factor parts in the denominator, which meets the requirements and formula of the split item: (2/(1*(1+2)))+(3/((1+2)*(1+2+3)) )+(4/((1+2+3)*(1+2+3+4)))+…+(100/((1+2+3+…+99)*(1+2+3 +…+100))) After calculating the simplification, what is the difference between its denominator and numerator?
分子是分母中两个因数部分的差符合裂项的要求和式：(2/(1*(1+2)))+(3/((1+2)*(1+2+3)))+(4/((1+2+3)*(1+2+3+4)))+…+(100/((1+2+3+…+99)*(1+2+3+…+100)))计算化简后得到一个最简分数，它的分母与分子之差为多少．
<gadget id="calculator">5_050 - 5_049</gadget>
<output>1</output>

<result>1</result>