June 17th, 2018, 04:39 AM  #1 
Member Joined: Oct 2012 Posts: 67 Thanks: 0  infinite series
Find 3/13+33/13^2+333/13^3+3333/13^4+.... 
June 17th, 2018, 06:35 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,171 Thanks: 1141 
write the series as $\displaystyle \sum \limits_{k=1} \dfrac{10^k1}{3\cdot 13^k}$ this is then the scaled difference of two geometric series whose values should be easy enough to compute. 

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