Question

Cho A = \(\frac{1}{1.2.3}\)+\(\frac{1}{2.3.4}\)+......+\(\frac{1}{18.19.20}\)

Chứng minh rằng: A < \(\frac{1}{4}\)

giúp mình nha, mình cần gấp!

Answer 1

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

A=1/2(1/1.2-1/19.20)

A=1/2(1/2-1/380)

A=1/2.189/380

A=189/760

Mà 189/760<1/4

=>A<1/4

Answer 2

A = \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+.....+\frac{1}{18.19.20}\)

2A = \(\frac{2}{1.2.3}+\frac{2}{2.3.4}+......+\frac{2}{18.19.20}\)

2A = \(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+.....+\frac{1}{18.19}-\frac{1}{19.20}\)

2A = \(\frac{1}{1.2}-\frac{1}{19.20}\)

2A =     \(\frac{189}{360}\)

 A = \(\frac{189}{360}:2\)

Vậy A = \(\frac{189}{760}<\frac{189}{756}=\frac{1}{4}\)

k nha?