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# Help

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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
+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

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Sep 14, 2018