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[tex]10S = 10 + 100 + 1000 + 10000 + 100000 + ... [/tex]

[tex]S - 10S = (1 + 10 + 100 + 1000 + 10000 + ...) - (10 + 100 + 1000 + 10000 + ...) [/tex]

[tex]-9S = 1 + (10 - 10) + (100 - 100) + (1000 - 1000) + (10000 - 10000) ... [/tex]

[tex]-9S = 1 + 0 + 0 + 0 + 0 + 0 ...[/tex]

[tex]-9S = 1 [/tex]

[tex]S = -1/9[/tex]

What's wrong (or right) with this?

Thanks,

Unit