Question

So Sánh:

1/1*2+1/2*3+1/3*4+..............+1/2007*2008 với 1

Answer 1

Ta có: \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2007.2008}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2007}-\frac{1}{2008}\)

\(=1-\frac{1}{2008}< 1\)

Answer 2

\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2007.2008}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2007}-\frac{1}{2008}=1-\frac{1}{2008}< 1\)

Answer 3

ta có : 

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+......+\frac{1}{2007.2008}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....\cdot+\frac{1}{2007}-\frac{1}{2008}\)

\(=1-\frac{1}{2008}\)

\(=\frac{2007}{2008}\)

ta thấy \(\frac{2007}{2008}< 1\)

\(\Rightarrow\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{2007.2008}< 1\)