Bài 1 

1, Ta có \(A=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+....+\frac{10}{1400}\)

\(A=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)

\(A=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+....+\frac{5}{25.28}\)

\(A=5.\left(\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+....+\frac{1}{25.28}\right)\)

\(A=5.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)

\(A=5.\left(\frac{1}{4}-\frac{1}{28}\right)=5.\frac{3}{14}=\frac{15}{14}\)

Vậy \(A=\frac{15}{14}\)

2, 

a) \(A=\frac{2n-7}{n-5}=\frac{2n-7-3+3}{n-5}=\frac{\left(2n-10\right)+3}{n-5}=\frac{3}{n-5}\)

Suy ra để A có giá trị nguyên thì \(n-5\inƯ\left(3\right)\)

Mà \(Ư\left(3\right)=\left\{1;-1;3;-3\right\}\)

Khi đó \(n-5\in\left\{1;-1;3;-3\right\}\)

Suy ra \(n\in\left\{6;4;8;2\right\}\)

Vậy ......

b) Ta có : \(A=\frac{2n-7}{n-5}=\frac{2n-7-3+3}{n-5}=\frac{\left(2n-10\right)+3}{n-5}=2+\frac{3}{n-5}\)

Để A có giá trị lớn nhất \(\Leftrightarrow\frac{2n-7}{n-5}\)lớn nhất \(\Leftrightarrow2+\frac{3}{n-5}\)lớn nhất \(\Leftrightarrow\frac{3}{n-5}\)lớn nhất \(\Leftrightarrow n=6\)

Khi đó A = 5 

 Vậy A đạt GTLN khi và chỉ khi n = 6

H=10/56+10/140+10/260+...+10/1400

H=10/56+10/1400

H=13/70

vay H=13/70

ai di qua nho h cho minh nhe

SAO MÀ DỐT THẾ ! DỄ THẾ NÀY MÀ LÀM KHÔNG ĐƯỢC

H = 10/56 + 10/140 + 10/260 + ... + 10/1400

H = 5/3 × (3/28 + 3/70 + 3/130 + ... + 3/700)

H = 5/3 × (3/4×7 + 3/7×10 + 3/10×13 + ... + 3/25×28)

H = 5/3 × (1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + ... + 1/25 - 1/28)

H = 5/3 × (1/4 - 1/28)

H = 5/3 × 3/14

H = 5/14

\(H=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+....+\frac{10}{1400}\)

   \(=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+....+\frac{5}{25.28}\)

   \(=\frac{5}{3}.\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+....+\frac{3}{25.28}\right)\)

    \(=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+....+\frac{1}{25}-\frac{1}{28}\right)\)

     \(=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{28}\right)\)

     \(=\frac{5}{3}.\frac{3}{14}=\frac{5}{14}\)

\(H=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+.....+\frac{10}{1400}\)

\(=\frac{5}{3}\times\left(\frac{3}{28}+\frac{3}{70}+....+\frac{3}{700}\right)\)

\(=\frac{5}{3}\times\left(\frac{3}{4}\times7+\frac{3}{7}\times10+.....+\frac{3}{25}\times28\right)\)

\(=\frac{5}{3}\times\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-....+\frac{1}{25}-\frac{1}{28}\right)\)

\(=\frac{5}{3}\times\left(\frac{1}{4}-\frac{1}{28}\right)\)

\(=\frac{5}{3}\times\frac{3}{14}=\frac{5}{14}\)

B = 10/56 + 10/140 + 10/260 + ...+ 10/1400      

B= 5/28 + 5/70 +.....+10/700 
= 5/(4.7)+5/(7.10)+....5/(25.28) 
3B= 5( 1/4 - 1/7 +1/7-1/10+......+1/25-1/28) 
3B = 5 (1/4-1/28) 
3B=15/14 
B = 15/14 : 3 

B = 5/14

Giúp tôi giải toán - Hỏi đáp, thảo luận về toán học - Học toán với OnlineMath

H = 10/56 + 10/140 + 10/260 +…..+ 10/1400
H = 5/28 + 5/70 + 5/130 +…..+ 5/700
H = 5 x (1/4.7 + 1/7.10 + 1/10.13 +…………+ 1/25.28)
H = 5/3 x (3/4.7 + 3/7.10 + 3/10.13 +………+ 3/25.28)
H = 5/3 x (1/4-1/7+1/7-1/10+1/10-1/13+……..+1/25-1/28)
H = 5/3 x (1/4-1/28)
H = 5/3 x 3/14 = 5/14 

= 5/ 14