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May 6th, 2017, 06:57 AM  #1 
Newbie Joined: May 2017 From: Italy Posts: 1 Thanks: 0  a problem with cubes
Hey all, will you reach 2 as sum of the length of sides if you put infinite cubes one on top of another (first one side is 1 and each cube is 1/10 of the previous one)? Last edited by skipjack; May 6th, 2017 at 04:20 PM. 
May 6th, 2017, 08:48 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,974 Thanks: 1026 
$s_0=1$ $s_i = \dfrac{s_{i1}}{10},~i,1,2,3, \dots$ $h=\displaystyle \sum_{i=0}^\infty~\left(\dfrac{1}{10}\right)^k$ $h=\dfrac{1}{1\frac{1}{10}} = \dfrac{10}{9} < 2$ 

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cubes, problem 
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