Question

Tính :B=2/1x2+2/2x3+2/3x4……+2/99x100

 

 

Answer 1

B = \(\dfrac{2}{1\times2}\) + \(\dfrac{2}{2\times3}\)+ \(\dfrac{2}{3\times4}\)+...+ \(\dfrac{2}{99\times100}\)

B = 2 \(\times\) ( \(\dfrac{1}{1\times2}\) + \(\dfrac{1}{2\times3}\)+ \(\dfrac{1}{3\times4}\)+....+ \(\dfrac{1}{99\times100}\))

B = 2 \(\times\) ( \(\dfrac{1}{1}\) - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\)+...+ \(\dfrac{1}{99}\) - \(\dfrac{1}{100}\))

B = 2 \(\times\) ( \(\dfrac{1}{1}\) - \(\dfrac{1}{100}\))

B = 2 \(\times\) \(\dfrac{99}{100}\)

B = \(\dfrac{99}{50}\)