Not hard

Algebra Level 3

11×2+12×3+13×4+......+199×100=ab\frac{1}{1 \times 2} +\frac{1}{2 \times 3}+\frac{1}{3 \times 4}+......+\frac{1}{99 \times 100}=\frac{a}{b} where ab\frac{a}{b} is in simplest fractional form. Find a+ba+b . After finding a+ba+b, express it in the form of n100xn100-x. What is n+xn+x ?

[Note: a,b,n,xZ+a,b,n,x\in\mathbb{Z^{+}} and 0<n,x<1000<n,x<100]

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