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Question Number 190521 by Rupesh123 last updated on 04/Apr/23

Answered by mehdee42 last updated on 04/Apr/23

8+88+888+...+888...8=8(((10−1)/9)+((10^2 −1)/9)+...+((10^n −1)/9)) =(8/9)(10+10^2 +...+10^n −n)=(8/9)(((10^(n+1) −10)/9)−n) ⇒lim_(n→∞) ((81)/(10^n ))×(8/9)(((10^(n+1) −10)/9)−n)=80

8+88+888+...+888...8=8(10−19+102−19+...+10n−19)=89(10+102+...+10n−n)=89(10n+1−109−n)⇒limn→∞8110n×89(10n+1−109−n)=80

Commented by Rupesh123 last updated on 04/Apr/23

Excellent, sir!

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