Question Number 194406 by Safojon last updated on 05/Jul/23
Answered by BaliramKumar last updated on 05/Jul/23
$$\mathrm{i}\:\mathrm{find}\:\mathrm{2007}^{\mathrm{th}} \:\mathrm{digit}\:=\:\mathrm{5} \\ $$
Commented by Safojon last updated on 05/Jul/23
$${prove}\:\:{thet}\:{sir}\:{pleas}. \\ $$
Answered by mr W last updated on 08/Jul/23
$$\mathrm{1}…\mathrm{9}\:\Rightarrow\mathrm{9}×\mathrm{1}=\mathrm{9} \\ $$$$\mathrm{10}…\mathrm{99}\:\Rightarrow\mathrm{90}×\mathrm{2}=\mathrm{180}\:\Rightarrow\mathrm{9}+\mathrm{180}=\mathrm{189} \\ $$$$\mathrm{100}…\mathrm{999}\:\Rightarrow\mathrm{900}×\mathrm{3}=\mathrm{2700}\:\Rightarrow\mathrm{2700}+\mathrm{189}=\mathrm{2889}\:>\mathrm{2007} \\ $$$$\mathrm{2007}−\mathrm{189}=\mathrm{1818} \\ $$$$\mathrm{1818}/\mathrm{3}=\mathrm{606} \\ $$$$\mathrm{99}+\mathrm{606}=\mathrm{705} \\ $$$$\Rightarrow{the}\:\mathrm{2007}^{{th}} \:{digit}\:{is}\:\mathrm{5}. \\ $$$$\mathrm{123}…\mathrm{704705706}…\mathrm{2007} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\uparrow\:{the}\:\mathrm{2007}^{{th}} \:{digit} \\ $$