My Math Forum a problem with cubes

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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 $s_0=1$ $s_i = \dfrac{s_{i-1}}{10},~i,1,2,3, \dots$ $h=\displaystyle \sum_{i=0}^\infty~\left(\dfrac{1}{10}\right)^k$ $h=\dfrac{1}{1-\frac{1}{10}} = \dfrac{10}{9} < 2$ Thanks from eltes

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