a) G = $\frac{1}{15}$ + $\frac{1}{35}$ + $\frac{1}{63}$ + ... + $\frac{1}{2499}$

Đáp án:

Giải thích các bước giải:

 `G = 1/15 + 1/35 + 1/63 +...+ 1/2499`

 `G = 1/(3 . 5) + 1/(5 . 7) + 1/(7 . 9) + ... + 1/(49 . 51)`

 `2 . G = 2. (1/(3 . 5) + 1/(5 . 7) +1/(7 . 9) + ... + 1/(49 . 51))`

 `2G = 2/(3 . 5) + 2/(5 . 7) + 2/(7 . 9) + ... + 2/(49 . 51)`

 `2G = (5 - 3)/(3 . 5) + (7 - 5)/(5 . 7) + (9 - 7)/(7 . 9) + .... + (51 - 49)/(49 . 51)`

 `2G = 5/(3 . 5) - 3/(3 . 5) + 7/(5 . 7) - 5/(5 . 7) + 9/(7 . 9) - 7/(7 . 9) + ....+ 51/(49 . 51) - 49/(49 . 51)`

 `2G = 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 +.... + 1/49 - 1/51`

 `2G = 1/3 - 1/51`

 `2G = 48/153 = 16/51`

 `G = 16/51 : 2 = 16/102 = 8/51`