\(5A=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{\left(5n+1\right).\left(5n+6\right)}\)
\(5A=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{5n+1}-\frac{1}{5n+6}\)
\(5A=1-\frac{1}{5n+6}=\frac{5n+6-1}{5n+6}=\frac{5n+5}{5n+6}\)=> \(A=\frac{n+1}{5n+6}\)
CTR:1/1*6+1/6*11+1/11*16+...+1/(5n+1)*(5n+6)=n+1/5n+6 (n thuoc N)
chứng minh
1/1x6+1/6x11+...+1/(5n+1)(5n-6)=3/11
1/1x2x3+1/2x3x4+...1/18x19x20<1/4
BT1:Chứng minh rằng với mọi n thuộc N ta luôn có: 1/1.6 + 1/6.11 + 1/11.16 + ... +1/(5n+1)(5n+6) = n+1/5n+6
BT 2 :Tìm x thuộc N biết: x - 20/11.13 - 20/13.15 - 20/15.17 - .... - 20/53.55 = 3/11
BT 3 : Tìm x thuộc N biết: 1/21 + 1/28 + 1/36 + ... + 2/x(x+1) = 2/9
Chứng minh 1/1.6+1/6.11+1/11.16+...+1/(5n+1)(5n+6)=n+1/5n+6
CMR:1/1x6+1/6x11+1/11x16+....+1/(5n+1)(5n+6)=n+1/5n+6
C/m rang voi n thuoc N ta co 1/6+1/66+1/176+…+1/(5n+1).(5n+6)=n+1/5n+6
Chứng minh: 1/1.6+1/6.11+...+1/(5n+1)(5n+6)=n+1/5n+6
Chung minh
1/1.6+1/11.16+............+1/(5n+1).(5n+6)=n+1/5n+6
\(\dfrac{1}{1.6}+\dfrac{1}{6.11}+\dfrac{1}{11.16}+....+\dfrac{1}{\left(5n+1\right).\left(5n+6\right)}=\dfrac{n+1}{5n+6}\)
