Question

2/2x3 + 2/3x4 + 2/4x5 + ... + 2/199x200

Answer 1

A = \(\dfrac{2}{2.3}\) + \(\dfrac{2}{3.4}\) + \(\dfrac{2}{4.5}\) + ... + \(\dfrac{2}{199.200}\)

A = 2. (\(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + \(\dfrac{1}{4.5}\) + ... + \(\dfrac{1}{199.200}\))

A = 2.(\(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) + ... + \(\dfrac{1}{199}\) - \(\dfrac{1}{200}\))

A = 2.(\(\dfrac{1}{2}\) - \(\dfrac{1}{200}\))

A = 2. \(\dfrac{99}{200}\)

A = \(\dfrac{99}{100}\)