Question

Tính:

a) C = 3/1.3 + 3/3.5 + 3/3.7 +...+ 3/49.51

b) D = 1/2 + 1/14 + 1/35 + 1/65 + 1/104 + 1/152

Answer 1

a; C = \(\dfrac{3}{1.3}\) + \(\dfrac{3}{3.5}\) + \(\dfrac{3}{3.7}\) + ... + \(\dfrac{3}{49.51}\)

   C = \(\dfrac{3}{2}\).(\(\dfrac{2}{1.3}\) + \(\dfrac{2}{3.5}\) + \(\dfrac{2}{5.7}\) + ... + \(\dfrac{2}{49.51}\))

  C = \(\dfrac{3}{2}\).(\(\dfrac{1}{1}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{7}\) + ... + \(\dfrac{1}{49}\) - \(\dfrac{1}{51}\))

 C = \(\dfrac{3}{2}\).(\(\dfrac{1}{1}\) - \(\dfrac{1}{51}\))

 C = \(\dfrac{3}{2}\).\(\dfrac{50}{51}\)

C = \(\dfrac{25}{17}\)