411522633744855...

hbghlyj

\[\frac{{{{10}^{3^3}} - 1}}{{3^5}} = {\rm{4115226337448559670781893}}\]
你发现什么规律?

tommywong

係唔係想話$243|(10^{27}-1)$啊？用LTE得㗎喇

hbghlyj

回复 2# tommywong \[{\left( {\frac{{10}}{3}} \right)^5} = \sum\limits_{i = 0}^\infty  {\left( {111i + 411} \right) \cdot {{10}^{ - 3i}}} \]
使用\[\sum\limits_{i = 0}^\infty  {\left( {ai + b} \right) \cdot {n^{ - i}}}  = \frac{{{\rm{n}}\left( {a{\rm{ + }}b\left( {n - 1} \right)} \right)}}{{{{\left( {n - 1} \right)}^2}}}\]在各种进制下写出更多的类似式子