Question Number 199729 by Mingma last updated on 08/Nov/23
Answered by mathfreak01 last updated on 08/Nov/23
$${N}\:=\:\underset{{n}\:=\:\mathrm{1}} {\overset{\mathrm{450}} {\sum}}\left(\mathrm{10}^{{n}} \:−\:\mathrm{1}\right) \\ $$$${N}\:=\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{450}} {\sum}}\mathrm{10}^{{n}} \:−\:\mathrm{450} \\ $$$${N}\:=\:\frac{\mathrm{10}\left(\mathrm{10}^{\mathrm{450}} \:−\:\mathrm{1}\right)}{\mathrm{9}}\:−\:\mathrm{450} \\ $$$${or} \\ $$$${N}\:=\:\left(\mathrm{10}\:−\:\mathrm{1}\right)\:+\:\left(\mathrm{100}\:−\:\mathrm{1}\right)\:+\:…\:+\:\left(\mathrm{1}\underset{\mathrm{450}\:{digits}} {\underbrace{\mathrm{00}…\mathrm{00}}}\:−\:\mathrm{1}\right) \\ $$$${N}\:=\:\underset{\mathrm{450}\:{digits}} {\underbrace{\mathrm{11}…\mathrm{11}}0}\:−\:\mathrm{450} \\ $$$${N}\:=\:\underset{\mathrm{447}\:{digits}} {\underbrace{\mathrm{11}..\mathrm{11}}1110}\:−\:\mathrm{450} \\ $$$${N}\:=\:\underset{\mathrm{447}\:{digits}} {\underbrace{\mathrm{11}..\mathrm{11}}0660} \\ $$$$ \\ $$
Commented by Rupesh123 last updated on 08/Nov/23
Perfect, sir!