Đặt biểu thức cần tính là A

(3/2)xA=3/8x11+3/11x14+...+3/290x293

(3/2)xA=(11-8)/8x11+(14-11)/11x14+...+(293-290)/290x293

(3/2)xA=1/8-1/11+1/11-1/14+...+1/290-1/293=1/8-1/293

A=[(1/8-1/293)x2]:3

A=1/5-1/8+1/8-1/11+...+1/602-1/605

=1/5-1/605

=24/121

\(B=\dfrac{3}{2\cdot5}+\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+...+\dfrac{3}{26\cdot29}\)

\(B=\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{26}-\dfrac{1}{29}\)

\(B=\dfrac{1}{2}-\dfrac{1}{29}\)

\(B=\dfrac{27}{58}\)

B= 3/2x5 + 3/5x8+ 3/8x11 + ... + 3/26x29

B= 1/2 - 1/5 + 1/5 - 1/8 + 1/8 - 1/11 + ... + 1/26 - 1/29

B= 1/2-1/29

B=27/58

\(\frac{1}{2\cdot5}+\frac{1}{5\cdot8}+\frac{1}{8\cdot11}+....+\frac{1}{97\cdot100}\)

\(=\frac{5-2}{2\cdot5}+\frac{8-5}{5\cdot8}+\frac{11-8}{8\cdot11}+...+\frac{100-97}{97\cdot100}\)

\(=\frac{1}{3}\cdot\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{97}-\frac{1}{100}\right)\)

\(=\frac{1}{3}\cdot\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(=\frac{1}{3}\cdot\frac{49}{100}=\frac{49}{300}\)

nhớ là phải có bài giải thì mới

Không biết làm nha. Mai đến lớp cô chữa

$\frac{2}{5\times 8}+\frac{2}{8\times 11}+\frac{2}{11\times 14}+...+\frac{2}{95\times 98}$

$=\left(\frac{3}{5\times 8}+\frac{3}{8\times 11}+\frac{3}{11\times 14}+...+\frac{3}{95\times 98}\right)\times \frac{2}{3}$

$=\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{14}+...+\frac{1}{95}-\frac{1}{98}\right)\times \frac{2}{3}$

$=\left(\frac{1}{5}-\frac{1}{98}\right)\times \frac{2}{3}$

$=\frac{93}{490}\times \frac{2}{3}$

$=\frac{93\times 2}{490\times 3}$

$=\frac{31\times 1}{245\times 1}$

$=\frac{31}{245}$

\(A=\dfrac{3}{5\times8}+\dfrac{3}{8\times11}+...+\dfrac{3}{2009\times2012}\)

\(A=\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{2009}-\dfrac{1}{2012}\)

\(=\dfrac{1}{5}-\dfrac{1}{2012}=\dfrac{2007}{10060}\)

giúp em với ạ

Ta có : A=3/2x5+3/5x8+3/8x11+3/11x14+3/14x17+3/17x20

     => A=1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+1/14-1/17+1/17-1/20

     => A=1/2-1/20

     => A=9/20

Vậy A=9/20

đó