Explicație pas cu pas:
4) suma are 100 de termeni:
[tex]\frac{1}{2} + \frac{11}{22} + \frac{111}{222} + ... + \frac{111...11}{222...22} = \\ = \frac{1}{2} + \frac{11 \cdot 1}{11 \cdot 2} + \frac{111 \cdot 1}{111 \cdot 2} + ... + \frac{111...11 \cdot 1}{111...11 \cdot 2} \\ = 101 \cdot \frac{1}{2} = 50[/tex]
5) suma are 101 termeni:
[tex]0.1 + 0.01 + 0.001 + ... + 0.000...01 = \\ = 0.11 + 0.001 + ... + 0.000...01 = ... \\ = 0.111... + .. + 0.000...01 = 0.111..11[/tex]
