a) 2/2.5 + 2/5.8 + 2/8.11 + ... + 2/x(x+3) = 7/23

3/2.5 + 3/5.8 + 3/8.11 + ... + 3/x(x+3) = 21/46

1/2 - 1/5 + 1/5 - 1/8 + 1/8 - 1/11 + ... + 1/x - 1/x+1 = 21/46

1/2 - 1/x+1 = 21/46

=> 1/x+1 = 1/23

=> x + 1 = 23

=> x = 22

Vậy x = 22.

b) 3/4 . x - 1/5 = 7/4 . x + 11/5

3/4 . x - 7/4 . x = 1/5 + 11/5

x (3/4 - 7/4) = 12/5

-x = 12/5

x = -12/5

Vậy x = -12/5.

\(\left(\dfrac{3}{2.5}+\dfrac{3}{5.8}+...+\dfrac{3}{17.20}\right).x=\dfrac{45}{23}\)
\(\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+....+\dfrac{1}{17}-\dfrac{1}{20}\right).x=\dfrac{45}{23}\)
\(\left(\dfrac{1}{2}-\dfrac{1}{20}\right).x=\dfrac{45}{23}\)
\(\dfrac{9}{20}\cdot x=\dfrac{45}{23}\)
\(x=\dfrac{45}{23}:\dfrac{9}{20}\)
\(x=\dfrac{100}{23}\)

\(\left(\dfrac{3}{2.5}+\dfrac{3}{5.8}+...+\dfrac{1}{17.20}\right)x=\dfrac{45}{23}\Leftrightarrow\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+...+\dfrac{1}{17}-\dfrac{1}{20}\right)x=\dfrac{45}{23}\)\(\Leftrightarrow\left(\dfrac{1}{2}-\dfrac{1}{20}\right)x=\dfrac{45}{23}\)

\(\Rightarrow\dfrac{9}{20}.x=\dfrac{45}{23}\)

\(\Rightarrow x=\dfrac{100}{23}\)

Chọn A

\(S=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{98.101}\)

\(S=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{98}-\frac{1}{101}\)

\(S=\frac{1}{2}-\frac{1}{101}\)

\(S=\frac{99}{202}\)

Bạn cho mình thêm 1/3 ở dòng 2 của bài làm mình nhé

Kết quả ra là : \(\frac{33}{202}\)

=chịu

tính như bình thường nha bạn. Có những câu đề bài là tính thuận tiện mà tính thường mk đã gặp nhiều rồi

2,140579710144928

S = 1/2.5 +1/5.8 +1/8.11+1/11.14+1/14.17+1/17.20

S=1/3.(1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+1/14-1/17+1/17-1/20)

S=1/3.(1/2-1/20)

S=1/3.(10/20-1/20)

S=1/3.9/20

S= 3/20

k nha

\(S=2.\left(\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{29.32}\right)\)

\(S=2.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{29}-\frac{1}{32}\right)\)

\(S=2.\left(\frac{1}{2}-\frac{1}{32}\right)\)

\(S=1-\frac{1}{16}< 1\)

Vậy \(S< 1\)

b

Chọn B