Question

Câu 1 : B = 1/3 + 1/6 + 1/10 + ... + 1/45

Câu 2 :  D = 3/1.3 + 3/3.5 + 3/5.7 + ... + 3/99.101

Câu 3 :  E= 4/1.3 + 4/3.5 + 5/5.7 + ... + 4/205.207

Câu 4 :  F= 1/1.4 + 1/4.7 + 1/10 + ...

- tổng này có 54 số hạng 

Câu 5 : G= 1/5 + 1/45 + 1/117 + 1/221

- tổng này có 54 số hạng

Answer 1

Câu 2:

\(D=\dfrac{3}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)

\(=\dfrac{3}{2}\cdot\dfrac{100}{101}=\dfrac{150}{101}\)

Câu 3: 

\(E=2\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{205}-\dfrac{1}{207}\right)\)

\(=2\cdot\left(1-\dfrac{1}{207}\right)=2\cdot\dfrac{206}{207}=\dfrac{412}{207}\)

Câu 5: 

\(G=\dfrac{1}{4}\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{17}\right)\)

\(=\dfrac{1}{4}\cdot\dfrac{16}{17}=\dfrac{4}{17}\)