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Question Number 194406 by Safojon last updated on 05/Jul/23

Answered by BaliramKumar last updated on 05/Jul/23

i find 2007^(th) digit = 5

$$\mathrm{i}\:\mathrm{find}\:\mathrm{2007}^{\mathrm{th}} \:\mathrm{digit}\:=\:\mathrm{5} \\ $$

Commented by Safojon last updated on 05/Jul/23

prove thet sir pleas.

$${prove}\:\:{thet}\:{sir}\:{pleas}. \\ $$

Answered by mr W last updated on 08/Jul/23

1...9 ⇒9×1=9 10...99 ⇒90×2=180 ⇒9+180=189 100...999 ⇒900×3=2700 ⇒2700+189=2889 >2007 2007−189=1818 1818/3=606 99+606=705 ⇒the 2007^(th) digit is 5. 123...704705706...2007 ↑ the 2007^(th) digit

$$\mathrm{1}...\mathrm{9}\:\Rightarrow\mathrm{9}×\mathrm{1}=\mathrm{9} \\ $$$$\mathrm{10}...\mathrm{99}\:\Rightarrow\mathrm{90}×\mathrm{2}=\mathrm{180}\:\Rightarrow\mathrm{9}+\mathrm{180}=\mathrm{189} \\ $$$$\mathrm{100}...\mathrm{999}\:\Rightarrow\mathrm{900}×\mathrm{3}=\mathrm{2700}\:\Rightarrow\mathrm{2700}+\mathrm{189}=\mathrm{2889}\:>\mathrm{2007} \\ $$$$\mathrm{2007}−\mathrm{189}=\mathrm{1818} \\ $$$$\mathrm{1818}/\mathrm{3}=\mathrm{606} \\ $$$$\mathrm{99}+\mathrm{606}=\mathrm{705} \\ $$$$\Rightarrow{the}\:\mathrm{2007}^{{th}} \:{digit}\:{is}\:\mathrm{5}. \\ $$$$\mathrm{123}...\mathrm{704705706}...\mathrm{2007} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\uparrow\:{the}\:\mathrm{2007}^{{th}} \:{digit} \\ $$

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