Question

Tính     S = \(\frac{1}{2.4}\)+\(\frac{1}{4.6}\)+\(\frac{1}{6.8}\)+.....+\(\frac{1}{98.100}\)

 

Answer 1

S = 1/2 . ( 1/2 -1/2 + 1/6 -1/2 + ...+ 1/99 - 1/100)

S= 1/2 . (1-2 - 1/100)

S=1/2 . 49/100

S= 49/200

 

Answer 2

\(S=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{98.100}\)

=>2S=\(2.\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{98.100}\right)\)

=\(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{98.100}\)

=\(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\)

=\(\frac{1}{2}-\frac{1}{100}=\frac{50}{100}-\frac{1}{100}=\frac{49}{100}\)

=>S=\(\frac{49}{100}:2=\frac{49}{100}.\frac{1}{2}=\frac{49}{200}\)

Answer 3

Ta co :

\(S=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{98.100}\)

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\)

\(=\frac{1}{2}-\frac{1}{100}\)

\(=\frac{49}{100}\)

Vay:\(S=\frac{49}{100}\)

Answer 4

Ta có:

\(S=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{98.100}\)

\(\Rightarrow S=\frac{1}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{98.100}\right)\)

\(\Rightarrow S=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\right)\)

\(\Rightarrow S=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(\Rightarrow S=\frac{1}{2}.\frac{49}{50}=\frac{49}{100}\)