Tính `G=1+9/45+9/105+9/189+…+9/29997`.

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1. $G$ $=$ $1$ $+$ $\frac{9}{45}$ $+$ $\frac{9}{105}$ $+$ $\frac{9}{189}$ $+$ $…$ $+$ $\frac{9}{29997}$ 

   $=$ $1$ $+$ $\frac{3}{15}$ $+$ $\frac{3}{35}$ $+$ $\frac{3}{63}$ $+$ $…$ $+$ $\frac{3}{9999}$ 

   $=$ $\frac{3}{1.3}$ $+$ $\frac{3}{3.5}$ $+$ $\frac{3}{5.7}$ $+$ $\frac{3}{7.9}$ $+$ $…$ $+$ $\frac{3}{99.101}$

   $=$ $\frac{3.2}{2.1.3}$ $+$ $\frac{3.2}{2.3.5}$ $+$ $\frac{3.2}{2.5.7}$ $+$ $\frac{3.2}{2.7.9}$ $+$ $…$ $+$ $\frac{3.2}{2.99.101}$

   $=$ $\frac{3}{2}$ $($ $\frac{2}{1.3}$ $+$ $\frac{2}{3.5}$ $+$ $\frac{2}{5.7}$ $+$ $\frac{2}{7.9}$ $+$ $…$ $+$ $\frac{2}{99.101}$ $)$

   $=$ $\frac{3}{2}$ $($ $1$ $-$ $\frac{1}{3}$ $+$ $\frac{1}{3}$ $-$ $\frac{1}{5}$ $+$ $\frac{1}{5}$ $-$ $\frac{1}{7}$ $+$ … $+$ $\frac{1}{99}$ $-$ $\frac{1}{101}$ $)$

   $=$ $\frac{3}{2}$ $($ $1$ $-$ $\frac{1}{101}$ $)$

   $=$ $\frac{3}{2}$ $.$ $\frac{100}{101}$ $=$ $\frac{150}{101}$ 

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2. `G = 1 + 9/45 + 9/105 + 9/189 + … + 9/29997`

   `G = 1 + (9 : 3)/(45 : 3) + (9 : 3)/(105 : 3) + (9 : 3)/(189 : 3) + … + (9 : 3)/(29997 : 3)`

   `G = 3/3 + 3/15 + 3/35 + 3/63 + … + 3/9999`

   `G = 3/(1 . 3) + 3/(5 . 3) + 3/(5 .7) + 3/(7 . 9) + … + 3/(99 . 101)`

   `G = 3/2 . (2/(1 . 3) + 2/(5 . 3) + 2/(5 . 7) + 2/(7 . 9) + … + 3/(99 . 101))`

   `G = 3/2 . (1 – 1/3 + 1/3 – 1/5 + 1/5 – 1/7 + 1/7 – 1/9 + … + 1/99 – 1/101)`

   `G = 3/2 . (1 – 1/101)`

   `G = 3/2 . 100/101`

   `G = 300/202`

   `G = 150/101`

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