Unusual infinite series

Calculus Level 3

If S=1+27+2579+252797+25257979+2525279797S=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=abS=\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 eππ2\approx \cfrac{e^{\pi}-\pi}{2} best problems soon. They are mostly challenging but all have very beautiful answers and computations

×

Problem Loading...

Note Loading...

Set Loading...