Question

[Nguyễn Anh Thái Dương]

Tính 

B=5/10.11+5/11.12+5/12.13+...+5/19.20

C=1/5.9+1/9.13+1/13.17+1/17.21+1/21.25

D=1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90

Cuu minh voi !!!!!!!

Answer 1

[Quỳnh Nguyễn]

\(B=\frac{5}{10.11}+\frac{5}{11.12}+\frac{5}{12.13}+...+\frac{5}{19.20}\)

\(B=5.\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+...+\frac{1}{19.20}\right)\)

\(B=5.\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{19}-\frac{1}{20}\right)\)

\(B=5.\left(\frac{1}{10}-\frac{1}{20}\right)\)

\(B=5.\frac{1}{20}=\frac{1}{4}\)

Answer 2

[Quỳnh Nguyễn]

\(C=\frac{1}{5.9}+\frac{1}{9.13}+\frac{1}{13.17}+\frac{1}{17.21}+\frac{1}{21.25}\)

\(4C=4.\left(\frac{1}{5.9}+\frac{1}{9.13}+\frac{1}{13.17}+\frac{1}{17.21}+\frac{1}{21.25}\right)\)

\(4C=\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+\frac{4}{17.21}+\frac{4}{21.25}\)

\(4C=\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{21}+\frac{1}{21}-\frac{1}{25}\)

\(4C=\frac{1}{5}-\frac{1}{25}=\frac{4}{25}\)

\(C=\frac{4}{25}:4=\frac{1}{25}\)