Question

tính

S=\(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{97\cdot99}\)

giúp mình các bạn ơi mình sắp học rồi nhanh nhanh mình tích cho

Answer 1

\(2S=\frac{2}{1}-\frac{2}{3}+\frac{2}{3}-\frac{2}{5}+...+\frac{2}{97}-\frac{2}{99}\)

\(2S=2-\frac{2}{99}\)

\(2S=\frac{196}{99}\)

\(S=\frac{196}{99}\cdot\frac{1}{2}=\frac{98}{99}\)

Answer 2

Ta có: S=2/1.3+2/3.5+...+2/97.99

S= 2/2.(1-1/3+1/3-1/5+...+1/97-1/99)

S= 1-1/99=98/99

Answer 3

\(S=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\)

\(2S=2\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{97.99}\right)\)

\(\Rightarrow S=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\)

\(S=1-\frac{1}{99}\)

\(S=\frac{98}{99}\)

Answer 4

S=\(\frac{2}{1.3}\)+\(\frac{2}{3.5}\)+\(\frac{2}{5.7}\)+...+\(\frac{2}{97.99}\)

  =1-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{5}\)+\(\frac{1}{5}\)-\(\frac{1}{7}\)+...+\(\frac{1}{97}\)-\(\frac{1}{99}\)

  =1-\(\frac{1}{99}\)

  =\(\frac{98}{99}\)

Vậy: S=\(\frac{98}{99}\)

Cách này là cách đơn giản nhất mà mk đã học về tính tổng một dãy phân số luôn đó nên cứ tin ở mk

Answer 5

\(S=2.\)\(\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+.....+\frac{1}{97.99}\right)\)

\(S=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{97}-\frac{1}{99}\)

\(S=\frac{1}{1}-\frac{1}{99}\)

\(S=\frac{98}{99}\)

Answer 6

\(S=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.....+\frac{2}{97}-\frac{2}{99}\)

\(S=1-\frac{1}{99}\)

\(S=\frac{99}{100}\)

Vậy \(S=\frac{99}{100}\)

Answer 7

\(S=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{97.99}\)

\(S=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{97}-\frac{1}{99}\)

\(S=1-\frac{1}{99}\)

\(S=\frac{98}{99}\)

Answer 8

\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\)

=\(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{97}-\frac{1}{99}\)

=\(1-\frac{1}{99}\)

=\(\frac{98}{99}\)

Vậy S=\(\frac{98}{99}\)