Question

cho biểu thức : A= 1/1x2 + 3/2x5+9/5x14+23/14x37+15/37x52+1967/42x2619 chững minh A<1

Answer 1

Ta có A = \(\frac{1}{1.2}+\frac{3}{2.5}+\frac{9}{5.14}+\frac{23}{14.37}+\frac{15}{37.52}+\frac{1967}{52.2019}\)(sửa lại đề)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{14}+\frac{1}{14}-\frac{1}{37}+\frac{1}{37}-\frac{1}{52}+\frac{1}{52}-\frac{1}{2019}\)

\(=1-\frac{1}{2019}=\frac{2018}{2019}< 1\)

=> A < 1 (ĐPCM)