Question

Chung minh rang A= \(\frac{1}{1.2.3}\) + \(\frac{1}{2.3.4}\) + \(\frac{1}{3.4.5}\) +......+ \(\frac{1}{18.19.20}\) < \(\frac{1}{4}\) ?

mình đang cần gấp !!!!!!!!!!!!!!!!!!!!

Answer 1

bài này chịu

Answer 2

2A = 2/1.2.3 + 2/2.3.4 + 2/3.4.5 + ... + 1/18.19.20

2A = 1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + 1/3.4 - 1/4.5 +...+1/18.19 - 1/19.20

2A =  1/1.2 - 1/19.20

2A = 1/2 - 1/19.20

A = (1/2 - 1/19.20) : 2

A = 1/4 - 1/(19.20.2)

MÀ 1/(19.20.2) > 0

nên A<1/4

Answer 3

1-1/2-1/3+1/2-1/3-1/4...1/19-1/20 =1-1/20<1/4