# Not hard

Algebra Level 3

$\frac{1}{1 \times 2} +\frac{1}{2 \times 3}+\frac{1}{3 \times 4}+......+\frac{1}{99 \times 100}=\frac{a}{b}$ where $$\frac{a}{b}$$ is in simplest fractional form. Find $$a+b$$ . After finding $$a+b$$, express it in the form of $$n100-x$$. What is $$n+x$$ ?

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

×