[tex]( \frac{1}{10} + \frac{2}{10} + \frac{3}{10} + .. + \frac{9}{10} ) + ( \frac{10}{100} + \frac{11}{100} + \frac{12}{100} + ... \frac{99}{100} ) \\ \\ = \frac{1 + 2 + 3 + ... + 9}{10} + \frac{10 + 11 + 12 + ... + 99}{100} \\ \\ = \frac{ \frac{9 \times (9 + 1)}{2} }{10} + \frac{(1 + 2 + 3 + ... + 99) - (1 + 2 + 3 + ... + 9}{100} \\ \\ = \frac{ \frac{9 \times 10}{2} }{10} + \frac{ \frac{99 \times (99 + 1)}{2} - \frac{9 \times (9 + 1)}{2} }{100} \\ \\ = \frac{45}{10} + \frac{(99 \times 50) - 45}{100} \\ \\ = \frac{45}{10} + \frac{4950 - 45}{100} \\ \\ = \frac{45}{10} + \frac{4905}{100} \\ \\ = \frac{450}{100} + \frac{4905}{100} \\ \\ = \frac{5355}{100} = 53.55[/tex]
