Question

[Tang Thien Dat]

Tinh gia tri cua bieu thuc \(D=\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}\)

Nho giai va trinh bay cach lam cho minh luon nha ^_^

Answer 1

[tran thanh minh]

1/2D=1/2(1/6+1/10+......+1/45)

1/2D=1/12+1/20+1/30+.....+1/90

1/2D=1/3.4+1/4.5+1/5.6+......+1/9.10

1/2D=1/3-1/4+1/4-1/5+1/5-1/6+....+1/9-1/10

1/2D=1/3-1/10

1/2D=7/30

D=7/30:1/2

D=7/15

Answer 2

[Nguyễn Văn Thi]

Ta có:\(D=\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}\)

\(=\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+\frac{2}{90}\)

\(=2.\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\right)\)

\(=2.\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\)

\(=2.\left(\frac{1}{3}-\frac{1}{10}\right)=2.\frac{7}{30}=\frac{7}{15}\)

Vậy \(D=\frac{7}{15}\)