# Unusual infinite series

**Calculus**Level 3

If \(S=1+\dfrac{2}{7}+\dfrac{2\cdot5}{7\cdot9}+\dfrac{2\cdot5\cdot2}{7\cdot9\cdot7}+\dfrac{2\cdot5\cdot2\cdot5}{7\cdot9\cdot7\cdot9}+\dfrac{2\cdot5\cdot2\cdot5\cdot2}{7\cdot9\cdot7\cdot9\cdot7}\cdots\)

And S can be represented by the form \(S=\dfrac{a}{b}\) for positive coprime integers a,b. Find a+b

This is just a quick filler problem. I'll be comming out with a set of my top \(\approx \cfrac{e^{\pi}-\pi}{2}\) best problems soon. They are mostly challenging but all have very beautiful answers and computations