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May 6th, 2017, 06:57 AM   #1
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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.
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May 6th, 2017, 08:48 AM   #2
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$s_0=1$

$s_i = \dfrac{s_{i-1}}{10},~i,1,2,3, \dots$

$h=\displaystyle \sum_{i=0}^\infty~\left(\dfrac{1}{10}\right)^k$

$h=\dfrac{1}{1-\frac{1}{10}} = \dfrac{10}{9} < 2$
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