Question

tính tổng:

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{13.15}\)

Answer 1

 

Đặt biểu thức trên là A, ta có:

\(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{13.15}\)

\(2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}\)

\(2A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{13}-\frac{1}{15}\)

\(2A=\frac{1}{1}-\frac{1}{15}\)

\(2A=\frac{14}{15}\Rightarrow A=\frac{14}{15}:2\Rightarrow A=\frac{7}{15}\)

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Answer 2

= 1 / 1 - 1/3 + 1 / 5 -1/7 + ....... +  1/13 - 1/15

= ( 1/1 - 1/15 ) 

= 1-1/15

= 14/15

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Answer 3

\(\frac{14}{15}\)

Answer 4

Gọi biểu thức đó là A

Ta có

A = \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{13.15}\) 

A x 2 = \(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}\)

A x 2 = \(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{13}-\frac{1}{15}\)

A x 2 =\(1-\frac{1}{15}\)

A x 2 = \(\frac{14}{15}\)

A = \(\frac{14}{15}:2\)

A = \(\frac{7}{15}\)

Đ/S : \(\frac{7}{15}\)

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Answer 5

1/1.3+1/3.5+1/5.7+...+1/13.15

=1/1-1/3+1/3-1/5+1/5-1/7+...+1/13-1/15

=1/1-1/15

=14/15

Answer 6

Đặt biểu thức trên là A, ta có:

\(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{13.15}\)

\(\Rightarrow2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}\)

\(\Rightarrow2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\)

\(\Rightarrow2A=1-\frac{1}{15}\)

\(\Rightarrow2A=\frac{14}{15}\)

\(\Rightarrow A=\frac{14}{15}\div2\)

\(\Rightarrow A=\frac{7}{15}\)

Answer 7

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Answer 8

Đặt \(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{13.15}\)

\(\Rightarrow2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}\)

\(\Rightarrow2A=\frac{1}{1}-\frac{1}{3}+...+\frac{1}{13}-\frac{1}{15}\)

\(\Rightarrow2A=1-\frac{1}{15}\)

\(\Rightarrow2A=\frac{14}{15}\)

\(\Rightarrow A=\frac{7}{15}\)

Vậy ...

Answer 9

\(\frac{1}{1.3}+\frac{1}{3.5}+..+\frac{1}{13.15}\)

\(=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{13.15}\right)\)

\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+..+\frac{1}{13}-\frac{1}{15}\right)\)

\(=\frac{1}{2}.\left(1-\frac{1}{15}\right)=\frac{1}{2}.\frac{14}{15}\)

\(=\frac{2.7}{2.15}=\frac{7}{15}\)

Answer 10

\(S=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{13.15}\)

\(2S=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\)

\(2S=1-\frac{1}{15}\)

\(2S=\frac{14}{15}\)

\(\Rightarrow S=\frac{14}{15}:2=\frac{7}{15}\)