#)Giải :

Ta có :

\(A=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}=5\left(\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{26.31}\right)\)

\(=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)=5\left(1-\frac{1}{31}\right)=5\times\frac{30}{31}=\frac{150}{31}>1\)

\(\Rightarrow A>1\)

Ta có: \(A=\frac{5^2}{1\cdot6}+\frac{5^2}{6\cdot11}+...+\frac{5^2}{26\cdot31}\)

\(=5\left(\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+...+\frac{5}{26\cdot31}\right)\)

\(=5\cdot\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)\)

\(=5\cdot\left(1-\frac{1}{31}\right)=5\cdot\frac{30}{31}=\frac{150}{31}>1\)

hay A>1(đpcm)

\(A=5.\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right)\)

\(A=5.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)\)

\(A=5.\left(1-\frac{1}{31}\right)\)

\(A=5.\frac{30}{31}\)

\(A=\frac{150}{31}>1\)

Đề hơi lạ nhỉ, vì quá rõ ràng rùi 5²/1.6 = 25/6 > 1 nên A lớn hơn 1

\(A=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)

   \(=5\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right)\)

   \(=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)\)

   \(=5\left(1-\frac{1}{31}\right)\)

    \(=5.\frac{30}{31}=\frac{150}{31}>1\)

=> A > 1

Study well ! >_<

Ta có : 

\(A=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)

\(A=5\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right)\)

\(A=5\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)\)

\(A=5\left(1-\frac{1}{31}\right)\)

\(A=5.\frac{30}{31}\)

\(A=\frac{150}{31}>1\)

\(\Rightarrow\)\(A>1\)

Vậy \(A>1\)

Chúc bạn học tốt ~ 

Ko cần dài dòng vậy đâu,A=\(\frac{5^2}{1.6}+\left(\frac{5^2}{6.11}+\frac{5^2}{11.16}+...+\frac{5^2}{26.31}\right)\)

Ta thấy \(\frac{5^2}{1.6}>1\)và tổng trong ngoặc >0  nên =>A>1

\(A=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)

\(A=5\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right)\)

\(A=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)\)

\(A=5\left(1-\frac{1}{31}\right)\)

\(A=5.\frac{30}{31}\)

\(A=\frac{150}{31}\)

\(\text{Vì }\frac{150}{31}>1\Rightarrow A>1\text{(đpcm)}\)

Chúc bạn học tốt !!!

1/3xD=1/(2x4)+1/(4x6)+...+1/(98x100)
2/3xD=2/(2x4)+2/(4x6)+...+1/(98x100)
2/3xD= 1/2-1/4+1/4-1/6+...+1/98-1/100
2/3xD=1/2-1/100
2/3xD=49/100
D=147/200

 

A=1/2+1/3+1/6+1/12
A=(1/2+1/3+1/6)+1/12
A=1+1/12
A=13/12

B=20/3+61/8+10/3+37/8
B=30/3+98/8
B=10+49/4
B=89/4

\(\Rightarrow A=5\left(\frac{1}{1x2}+\frac{1}{2x3}+...+\frac{1}{99x100}\right)\)

\(\Rightarrow A=5\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(\Rightarrow A=5\left(1-\frac{1}{100}\right)\)

\(\Rightarrow A=\frac{5x99}{100}=\frac{99}{20}\)

\(A=\frac{5}{1}-\frac{5}{2}+\frac{5}{2}-\frac{5}{3}+\frac{5}{3}-\frac{5}{4}+....+\frac{5}{99}-\frac{5}{100}\)

\(A=\frac{5}{1}+\left(-\frac{5}{2}+\frac{5}{2}\right)+\left(-\frac{5}{3}+\frac{5}{3}\right)+\left(-\frac{5}{4}+\frac{5}{4}\right)+...\left(-\frac{5}{99}+\frac{5}{99}\right)+\frac{5}{100}\)

\(A=\frac{5}{1}+0+0+....+0+\frac{5}{100}\)

\(A=\frac{500}{100}+\frac{5}{100}=\frac{205}{100}=\frac{101}{20}\)

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a) áp dụng dãy số cách đều đi

a, 1+6+11+16+...+46+51

Số số hạng là : (51-1):5+1 = 11 ( số )

Tổng là : (51+1).11:2=286

b, Đặt A = \(\dfrac{5^2}{1.6}+\dfrac{5^2}{6.11}+\dfrac{5^2}{11.16}+\dfrac{5^2}{16.21}+\dfrac{5^2}{21.26}+\dfrac{5^2}{26.31 } \)

\(\dfrac{1}{5}A=\) \(\dfrac{5}{1.6}+\dfrac{5}{6.11}+\dfrac{5}{11.16}+\dfrac{5}{16.21}+\dfrac{5}{21.26}+\dfrac{5}{26.31}\)

\(\dfrac{1}{5}A=\) \(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{31}\)

\(\dfrac{1}{5}A=1-\dfrac{1}{31}\)

\(\dfrac{1}{5}A=\dfrac{30}{31}\)

\(A=\dfrac{30}{31}:\dfrac{1}{5}=\dfrac{150}{31}\)

Vậy..