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$$

\begin{array}{r r@{}c@{}l}

& 1 &.& 11111111\ldots \\

& 0 &.& 11111111\ldots \\

& 0 &.& 01111111\ldots \\

& 0 &.& 00111111\ldots \\

& 0 &.& 00011111\ldots \\

& 0 &.& 00001111\ldots \\

& 0 &.& 00000111\ldots \\

+ &&\vdots \\ \hline &&& ~~~?

\end{array}

$$

 

 

 

\(\begin{array}{r r@{}c@{}l} & 1 &.& 11111111\ldots \\ & 0 &.& 11111111\ldots \\ & 0 &.& 01111111\ldots \\ & 0 &.& 00111111\ldots \\ & 0 &.& 00011111\ldots \\ & 0 &.& 00001111\ldots \\ & 0 &.& 00000111\ldots \\ + &&\vdots \\ \hline &&& ~~~? \end{array}\)
 

 Sep 14, 2018
edited by Alan  Sep 14, 2018
edited by Alan  Sep 14, 2018
edited by Alan  Sep 14, 2018
 #1
avatar+27529 
+1

If this is base 2 then it is equivalent to:  2 + 1 + 1/2 + 1/4 + 1/8 + ... = 4

 

If it is base 10 then it is equivalent to:  10/9 + 1/9 + 1/90 + 1/900 + ... = 100/81

.

 Sep 14, 2018

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