\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}+\frac{1}{99.100}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}=\frac{99}{100}\)
vì \(\frac{99}{100}< 1\)
nên \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}< 1\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}< 1\)
Vậy A<1
Ta có: \(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)
=>\(A=1-\frac{1}{100}\)
Vì \(\frac{1}{100}>0\Rightarrow\)\(1-\frac{1}{100}< 1\)hay A<1
A = \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{98.99}+\frac{1}{99.100}\)
A = \(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)
A = 1-\(\frac{1}{100}\)
A = \(\frac{99}{100}\)
=> A<1
Ta có : A = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +.......+1/98 - 1/99 + 1/99 - 1/100
=> A = 1 - 1/100
Vi 1/100 > 0 => 1 - 1/100 < 1 hay A < 1
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