Question Number 12190 by tawa last updated on 16/Apr/17
$$\mathrm{Show}\:\mathrm{that},\:\:\mathrm{0}.\mathrm{9999999999999}\:......\:\infty\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{1} \\ $$
Answered by ridwan balatif last updated on 16/Apr/17
$$\mathrm{let}\:\mathrm{0}.\mathrm{9999999}....=\mathrm{p} \\ $$$$\mathrm{0}.\mathrm{999999}...=\mathrm{p} \\ $$$$−−−−−−−−×\mathrm{10} \\ $$$$\mathrm{9}.\mathrm{9999}...=\mathrm{10p} \\ $$$$\mathrm{9}+\mathrm{0}.\mathrm{999}...=\mathrm{10p} \\ $$$$\mathrm{9}+\mathrm{p}=\mathrm{10p} \\ $$$$\mathrm{9}=\mathrm{9p} \\ $$$$\mathrm{p}=\mathrm{1} \\ $$
Commented by tawa last updated on 16/Apr/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$