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2014-10-05T15:05:59+03:00

9    =    10  -  1

99  =    10² - 1

999 =   10³ - 1

........................

99.......9 = 10^3242 -1  ⇒ S = (10+10²+10³+......+10^3242 )-1×3242          S1= 10+10² +10³ +............+10^3242 ⇒10S1 = 10² + 10³ +......+10^3243 ⇒10S1-S1= 9S1 = 10^3243 -10 ⇒ S=10^3243 - 10 - 3242                     ⇒S=10^3243-3252