Question

\(\frac{1}{11.13}+\frac{1}{13.15}+\frac{1}{15.17}+........+\frac{1}{19.21}\)

Answer 1

Gọi dãy trên là A

\(\Leftrightarrow2A=\frac{2}{11\cdot13}+\frac{2}{13\cdot15}+...+\frac{2}{19\cdot21}\)

\(\Leftrightarrow2A=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\)

\(\Leftrightarrow2A=\frac{1}{11}-\frac{1}{21}+0+...+0\)

\(\Leftrightarrow2A=\frac{10}{231}\)

\(\Leftrightarrow A=\frac{5}{231}\)

Answer 2

bài này dễ quá à

Answer 3

dễ thì làm đi lại còn nói

Answer 4

Bái này lp 6 bọn mk lm suốt r`. Nó cx ko khó lắm đâu bn. Dễ mà.

Học tốt.

Answer 5

cam on ban bonking

Answer 6

1/11*13 + 1/13*15 + 1/15*17 + ... + 1/19*21

= 1/2(2/11*13 + 2/13*15 + 2/15*17 + ... + 2/19*21)

= 1/2(1/11 - 1/13 + 1/13 - 1/15 + 1/15 - 1/17 + ... + 1/19 - 1/21)

= 1/2(1/11 - 1/21)

= 1/2*10/231

= bn tự tính nốt

Answer 7

\(\frac{1}{11.13}+\frac{1}{13.15}+\frac{1}{15.17}+...+\frac{1}{19.21}\) \(=\frac{1}{2}\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}+...+\frac{1}{19}-\frac{1}{21}\right)\)

\(=\frac{1}{2}\left(\frac{1}{11}-\frac{1}{21}\right)=\frac{1}{2}.\frac{10}{231}=\frac{5}{231}\)

Answer 8

\(\frac{1}{11.13}+\frac{1}{13.15}+\frac{1}{15.17}+...+\frac{1}{19.21}\)

\(=\frac{1}{2}.\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{19}-\frac{1}{21}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{11}-\frac{1}{21}\right)\)

\(=\frac{1}{2}.\frac{10}{231}\)

\(=\frac{5}{231}\)

Answer 9

\(\frac{1}{11.13}+\frac{1}{13.15}+\frac{1}{15.17}+...+\frac{1}{19.21}\)

= \(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{19}-\frac{1}{21}\)

= \(\frac{1}{11}-\frac{1}{21}\)

=\(\frac{10}{231}\)

~~~

#Suns

Answer 10

gọi \(\frac{1}{11.13}+\frac{1}{13.15}+\frac{1}{15.17}+......+\frac{1}{19.21}\)  là A

2A= \(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+......+\frac{2}{19.21}\)

2A= \(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+......+\frac{1}{19}-\frac{1}{21}\)

2A= \(\frac{1}{11}-\frac{1}{21}\)

2A= \(\frac{10}{231}\)

A= \(\frac{5}{231}\)

CHÚC BẠN HỌC TỐT

Answer 11

\(2A=\frac{2}{11.13}+\frac{2}{13.15}+....+\frac{2}{19.21}\)

\(2A=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+....+\frac{1}{19}-\frac{1}{21}\)

\(2A=\frac{1}{11}-\frac{1}{21}=\frac{10}{231}\)

\(A=\frac{10}{\frac{231}{2}}=\frac{20}{231}\)

Answer 12

\(S=\frac{1}{11.13}+\frac{1}{13.15}+...+\frac{1}{19.21}\)

\(2S=\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\)

\(2S=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\)

\(2S=\frac{1}{11}-\frac{1}{21}=\frac{10}{231}\)

\(S=\frac{10}{231}:2=\frac{5}{231}\)

Answer 13

Gọi dãy số trên là A

\(2A=\frac{2}{11.13}+\frac{2}{13.15}+....+\frac{2}{19.21}\)

\(2A=\frac{2}{11}-\frac{2}{13}+\frac{2}{13}-\frac{2}{15}+...+\frac{2}{19}-\frac{2}{21}\)

\(2A=\frac{2}{11}-\frac{2}{21}=\frac{20}{231}\)

\(\Rightarrow A=\frac{20}{231}:2=\frac{10}{231}\)

Answer 14

\(\frac{1}{11.13}+\frac{1}{13.15}+\frac{1}{15.17}+...+\frac{1}{19.21}\)

\(=\frac{1}{2}\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{19.21}\right)\)

\(=\frac{1}{2}\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{19}-\frac{1}{21}\right)\)

\(=\frac{1}{2}\left(\frac{1}{11}-\frac{1}{21}\right)\)

\(=\frac{1}{2}.\frac{10}{231}=\frac{5}{231}\)