1/3.[1-1/4+1/4-1/7+......+1/67-1/70]
=1/3.[1-1/70]
=1/3.69/70=23/70<1
xong roi k di
=(1-1/4)+(1/4-1/7)+....+(1/67-1/70)
=1-1/4+1/4-1/7+......+1/67-1/70
=1-1/70
=69/70
đúng 100%
=1/3.(3/1.4+3/4.7+...+3/67.70)
=1/3.(1/1-1/4+1/7-1/10+...+1/67-1/70)
=1/3.(1-1/70)
=1/3.(69/70)
=23/70<1
=\(\frac{1}{3}\times\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+.....+\frac{1}{67}-\frac{1}{70}\right)\)
=\(\frac{1}{3}\times\left(1-\frac{1}{70}\right)\)
=\(\frac{1}{3}\times\frac{69}{70}\)
=\(\frac{23}{70}\), MÀ 23/70 <1
\(\Rightarrow\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{69.70}\)< 1
CMR : \(\frac{1}{1\cdot4}+\frac{1}{4\cdot7}+\frac{1}{7\cdot10}+...+\frac{1}{67\cdot70}< 1\)
\(\Rightarrow\frac{1}{3}\cdot\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-...+\frac{1}{67}-\frac{1}{70}\right)< 1\)
\(\Rightarrow\frac{1}{3}\cdot\frac{69}{70}\)
\(\Rightarrow\frac{69}{210}< 1\left(đpcm\right)\)
