Question

Tính S biết :

\(S=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{99.101}\)

Answer 1

\(\Leftrightarrow S=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)

\(\Rightarrow S=\frac{1}{3}-\frac{1}{101}\)

\(\Rightarrow S=\frac{98}{303}\)

Answer 2

1/3.5 + 1/5.7 + ... + 1/99.101 

= 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/99 - 1/101 

= 1/3 - 1/101 

= 98/303 

Answer 3

sa cả

Answer 4

 \(2S=2\left(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{99.100}\right)\)

\(2S=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}+\frac{1}{100}\)

\(2S=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.100}\)

\(2S=\frac{1}{3}-\frac{1}{100}=\frac{97}{100}\)

\(S=\frac{97}{100}:2=\frac{97}{200}\)

Answer 5

S=\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9} +.....+\frac{1}{99.101}\)

S=\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{99}-\frac{1}{101}\)

S=\(\frac{1}{3}-\frac{1}{101}=\frac{101}{303}-\frac{3}{101}\)

S=\(\frac{98}{303}\)

Vậy tổng trên là \(\frac{98}{303}\)