#)Giải :

\(S=\frac{38}{25}+\frac{9}{10}-\frac{11}{15}+\frac{13}{21}-\frac{15}{28}+\frac{17}{36}-\frac{19}{45}+...-\frac{119}{4950}\)

\(S=\frac{38}{25}+\left(\frac{9}{10}-\frac{11}{15}\right)+\left(\frac{13}{21}-\frac{15}{28}\right) +\left(\frac{17}{36}-\frac{19}{45}\right)+...+\left(\frac{197}{4851}-\frac{199}{4950}\right)\)

Ta thấy : 

\(\left(\frac{9}{10}-\frac{11}{15}\right)=\frac{1}{6}=\frac{1}{\left(2.3\right)}=\frac{1}{2}-\frac{1}{3}\)

\(\left(\frac{13}{21}-\frac{15}{28}\right)=\frac{1}{12}=\frac{1}{\left(3.4\right)}=\frac{1}{3}-\frac{1}{4}\)

\(\left(\frac{17}{36}-\frac{19}{45}\right)=\frac{1}{20}=\frac{1}{\left(4.5\right)}=\frac{1}{4}-\frac{1}{5}\)

..........................................................

\(\left(\frac{197}{4851}-\frac{199}{4950}\right)=\frac{1}{2450}=\frac{1}{\left(49.50\right)}=\frac{1}{49}-\frac{1}{50}\)

\(\Rightarrow S=\frac{38}{25}+\left[\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)+...+\left(\frac{1}{49}-\frac{1}{50}\right)\right]\)

\(\Rightarrow S=\frac{38}{25}+\left[\frac{1}{2}-\frac{1}{50}\right]\)

\(\Rightarrow S=\frac{38}{25}+\frac{24}{50}\)

\(\Rightarrow S=2\)

                #~Will~be~Pens~#

123456789/1263859

bỏ tạm 38/25 ra 

=(9/10-11/15) +(13/21-15/28) +(197/4851-199/4950)

=1/6+1/12+1/20+...+1/49*50=2450

=3-2/2x3+4-3/3x4+5-4/4x5+....50-49/49x50

=1/2-1/3+1/3-...-1/50

1/2-1/50=12/25

=38/25+12/25=50/25

=2

Ta nhóm các số hạng từ thứ hai trở đi thành từng cặp: ( C = \frac{38}{25} + \left( \frac{9}{10} - \frac{11}{15} \right) + \left( \frac{13}{21} - \frac{15}{28} \right) + ... + \left( \frac{197}{4851} - \frac{199}{4950} \right) ) Tính tổng mỗi cặp: Cặp tổng quát thứ (n): ( \frac{2n+7}{(n+1)(2n+3)} - \frac{2n+9}{(n+2)(2n+3)} ) cho (n=1, 2, 3, ... ) Với (n=1): ( \frac{9}{10} - \frac{11}{15} = \frac{1}{6} = \frac{1}{2 \times 3} ) Với (n=2): ( \frac{13}{21} - \frac{15}{28} = \frac{1}{12} = \frac{1}{3 \times 4} ) Với (n=48): ( \frac{197}{4851} - \frac{199}{4950} = \frac{1}{2450} = \frac{1}{49 \times 50} ) Tổng các cặp là ( S' = \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + ... + \frac{1}{49 \times 50} = \sum_{n=2}^{49} \frac{1}{n(n+1)} = \sum_{n=2}^{49} \left( \frac{1}{n} - \frac{1}{n+1} \right) = \frac{1}{2} - \frac{1}{50} = \frac{24}{50} = \frac{12}{25} ). ( C = \frac{38}{25} + \frac{12}{25} = \frac{50}{25} = 2 ). Đáp án: 2

9/120 nha bạn

bỏ tạm 38/25 ra 

=(9/10-11/15) +(13/21-15/28) +(197/4851-199/4950)

=1/6+1/12+1/20+...+1/49*50=2450

=3-2/2x3+4-3/3x4+5-4/4x5+....50-49/49x50

=1/2-1/3+1/3-...-1/50

1/2-1/50=12/25

=38/25+12/25=50/25

=2

\(S=\frac{38}{25}+\frac{9}{10}-\frac{11}{15}+\cdot\cdot\cdot+\frac{197}{4851}-\frac{199}{4950}\)

\(\Rightarrow S=\frac{38}{25}+\frac{18}{20}-\frac{22}{30}+\cdot\cdot\cdot+\frac{394}{9702}-\frac{398}{9900}\)

\(\Rightarrow S=\frac{38}{25}+2\cdot\left(\frac{9}{20}-\frac{11}{30}+\cdot\cdot\cdot+\frac{197}{9702}-\frac{199}{9900}\right)\)

\(\Rightarrow S=\frac{38}{25}+2\cdot\left(\frac{9}{4\cdot5}-\frac{11}{5\cdot6}+\cdot\cdot\cdot+\frac{197}{98\cdot99}-\frac{199}{99\cdot100}\right)\)

\(\Rightarrow S=\frac{38}{25}+2\cdot\left(\frac{1}{4}+\frac{1}{5}-\frac{1}{5}-\frac{1}{6}+\cdot\cdot\cdot-\frac{1}{99}-\frac{1}{100}\right)\)

\(\Rightarrow S=\frac{38}{25}+2\cdot\left(\frac{1}{4}-\frac{1}{100}\right)\)

\(\Rightarrow S=\frac{38}{25}+2\cdot\left(\frac{25}{100}-\frac{1}{100}\right)\)

\(\Rightarrow S=\frac{38}{25}+2\cdot\frac{24}{100}\)

\(\Rightarrow S=\frac{38}{25}+2\cdot\frac{6}{25}\)

\(\Rightarrow S=\frac{38}{25}+\frac{12}{25}\)

\(\Rightarrow S=\frac{50}{25}=2\)

bỏ tạm 38/25 ra 

=(9/10-11/15) +(13/21-15/28) +(197/4851-199/4950)

=1/6+1/12+1/20+...+1/49*50=2450

=3-2/2x3+4-3/3x4+5-4/4x5+....50-49/49x50

=1/2-1/3+1/3-...-1/50

1/2-1/50=12/25

=38/25+12/25=50/25

=2

hello

A= 38/25+9/10-11/15+13/21-15/28+17/36-...+197/4851-199/4950

Ta có thể viết lại : (9/20-11/15)+(13/21-15/28)+17/36-19/45...+(197/4851-199/4950)

Ta thấy:(9/10-11/15)=1/6=1/2x3=1/2-1/3

(13/21-15/28)=1/12=1/3x4=1/3-1/4

(17/36-19/45)=1/20=1/4x5=1/4-1/5

............................

Ta được:9/10-11/15+13/21-15/28+17/36-19/45...+197/4851-199/4950=1/2-1/3+1/3-1/4+1/4-1/5=24/50

Vậy:A= 38/25+24/50

A=2

A=2 nhé bạn

2 nha bạn nhé