Question

TÍNH:

\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{9999}\)

GIÚP MÌNH VỚI, MIK SẼ TICK CHO!!!

 

Answer 1

\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+....+\frac{1}{9999}\)

=\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+....+\frac{1}{99.101}\)

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

=\(1-\frac{1}{101}=\frac{100}{101}\)

Answer 2

tích trước đi đã!!!!!!!!!

Answer 3

\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{9999}\)

\(2\left(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+...+\frac{2}{9999}\right)\)

\(2\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(2\left(1-\frac{1}{101}\right)\)

\(2\times\frac{100}{101}\)

\(\frac{200}{101}\)

Answer 4

=\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{99.101}\)

= 2(\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\))

= 2(\(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\))

= 2(\(\frac{1}{1}-\frac{1}{101}\))

= .\(2.\frac{100}{101}\)

= \(\frac{50}{101}\)

Answer 5

\(\frac{100}{101}\)nha !

Answer 6

đặt 

\(A=\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{9999}\)

      \(=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{99.101}\)

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

         \(=1-\frac{1}{101}=\frac{100}{101}\)

\(\Rightarrow A=\frac{100}{101}\)

chúc bạn hok tốt!