Question

[Linh Dan Pham]

Tính Tổng:

S1= 5/10.11+ 5/11.12+....+5/14.15

S2= 1/5.9+1/9.13+1/13.17+...+1/21.25

Answer 1

[Nguyễn Thanh Hằng]

\(S1=\dfrac{5}{10.11}+\dfrac{5}{11.12}+.............+\dfrac{5}{14.15}\)

\(\Leftrightarrow S1=5\left(\dfrac{1}{10.11}+\dfrac{1}{11.12}+...............+\dfrac{1}{14.15}\right)\)

\(\Leftrightarrow S1=5\left(\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+.............+\dfrac{1}{14}-\dfrac{1}{15}\right)\)

\(\Leftrightarrow S1=5\left(\dfrac{1}{10}-\dfrac{1}{15}\right)\)

\(\Leftrightarrow S1=5.\dfrac{1}{30}=\dfrac{1}{6}\)

\(S2=\dfrac{1}{5.9}+\dfrac{1}{9.13}+\dfrac{1}{13.17}+........+\dfrac{1}{21.25}\)

\(\Leftrightarrow4S_2=\dfrac{4}{5.9}+\dfrac{4}{9.13}+..............+\dfrac{4}{21.25}\)

\(\Leftrightarrow4S_2=\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+............+\dfrac{1}{21}-\dfrac{1}{25}\)

\(\Leftrightarrow4S_2=\dfrac{1}{5}-\dfrac{1}{25}\)

\(\Leftrightarrow4S_2=\dfrac{4}{25}\)

\(\Leftrightarrow S_2=\dfrac{16}{25}\)