Question

[vũ hoài thu]

\(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)

Answer 1

[soyeon_Tiểu bàng giải]

1/21 + 1/28 + 1/36 + ... + 2/x(x + 1) = 2/9

1/2 × (1/21 + 1/28 + 1/36 + ... + 2/x(x + 1) = 1/2 × 2/9

1/42 + 1/56 + 1/72 + ... + 1/x(x + 1) = 1/9

1/6×7 + 1/7×8 + 1/8×9 + ... + 1/x(x + 1) = 1/9

1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 + ... + 1/x - 1/x + 1 = 1/9

1/6 - 1/x + 1 = 1/9

1/x + 1 = 1/6 - 1/9

1/x + 1 = 3/18 - 2/18

1/x + 1 = 1/18

=> x + 1 = 18

=> x = 18 - 1

=> x = 17