P=2(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)

P=2((1/2*3)+(1/3*4)+(1/4*5)+(1/5*6)+(1/6*7)+(1/7*8)+(1/8*9)+(1/9*10)

P=2(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10)

P=2(1/2-1/10)

P=2*2/5

P=4/5

H NHA.

\(\frac{1}{2}\) E= \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\)

\(\frac{1}{2}\) E = \(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{8.9}\)

\(\frac{1}{2}E\) = \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}\)

\(\frac{1}{2}E\) = \(\frac{1}{2}-\frac{1}{9}\)

\(\frac{1}{2}E\) =\(\frac{7}{18}\)

=> E = \(\frac{7}{9}\)

E=\(\frac{1}{3}+\frac{1}{6}+....+\frac{1}{28}+\frac{1}{36}\)

\(\frac{1}{2}E=\frac{1}{6}+\frac{1}{12}+...+\frac{1}{56}+\frac{1}{72}\)

\(\frac{1}{2}E=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{7.8}+\frac{1}{8.9}\)

\(\frac{1}{2}E=\frac{3-2}{2.3}+\frac{4-3}{3.4}+...\frac{8-7}{7.8}+\frac{9-8}{8.9}\)

\(\frac{1}{2}E=\frac{3}{2.3}-\frac{2}{2.3}+\frac{4}{3.4}-\frac{3}{3.4}+...+\frac{8}{7.8}-\frac{7}{7.8}+\frac{9}{8.9}-\frac{8}{8.9}\)

\(\frac{1}{2}E=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)

\(\frac{1}{2}E=\frac{1}{2}-\frac{1}{9}=\frac{7}{18}\)

E=\(\frac{7}{18}:\frac{1}{2}=\frac{7}{9}\)

a: \(A=\left(\frac{136}{15}-\frac{28}{5}+\frac{62}{10}\right)\cdot\frac{21}{24}\)

\(=\left(\frac{272}{30}-\frac{168}{30}+\frac{186}{30}\right)\cdot\frac78\)

\(=\frac{290}{30}\cdot\frac78=\frac{29}{3}\cdot\frac78=\frac{203}{24}\)

b: \(B=\frac56+6\frac56\left(11\frac{5}{20}-9\frac14\right):8\frac13\)

\(=\frac56+\frac{41}{6}\cdot\left(11+\frac14-9-\frac14\right):\frac{25}{3}=\frac56+\frac{41}{6}\cdot2\cdot\frac{3}{25}\)

\(=\frac56+\frac{41}{25}=\frac{125}{150}+\frac{246}{150}=\frac{371}{150}\)

c: \(C=1+3+6+\cdots+1225\)

\(=\frac12\left(2+6+12+\cdots+2450\right)=\frac12\cdot\left(1\cdot2+2\cdot3+\cdots+49\cdot50\right)\)

\(=\frac12\cdot\left\lbrack1\left(1+1\right)+2\left(2+1\right)+\cdots+49\left(49+1\right)\right\rbrack=\frac12\cdot\left\lbrack\left(1+2+\cdots+49\right)+\left(1^2+2^2+\cdots+49^2\right)\right\rbrack\)

\(=\frac12\cdot\left\lbrack49\cdot\frac{50}{2}+\frac{49\left(49+1\right)\left(2\cdot49+1\right)}{6}\right\rbrack\)

\(=\frac12\cdot\left\lbrack49\cdot25+49\cdot50\cdot\frac{99}{6}\right\rbrack=\frac12\cdot\left\lbrack49\cdot25+49\cdot25\cdot33\right\rbrack=\frac12\cdot49\cdot25\cdot\left(33+1\right)\)

\(=49\cdot25\cdot\frac{34}{2}=49\cdot25\cdot17=20825\)

ta có 
1/2 P=1/2(1-1/10-1/15-1/3-1/28-1/6-1/21)
=1/2-(1/6+1/12+1/20+1/30+1/42+1/56)
=1/2-(1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8)
=1/2-(1/2-1/8)
=1/8
suy ra P=1/4

ta có 
1/2 P=1/2(1-1/10-1/15-1/3-1/28-1/6-1/21)
=1/2-(1/6+1/12+1/20+1/30+1/42+1/56)
=1/2-(1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8)
=1/2-(1/2-1/8)
=1/8
suy ra P=1/4

A=/x-2/+3x+2

1 x 3 x 5 + 2 x 6 x 10 + 3 x 9 x 15/3 x 5 x 12 + 6 x 10 x 24 + 9 x 15 x 36 = 15 + 120 + 8100 + 1440 + 4860 = 14535

\(\frac{1\times3\times5+2\times6\times10+3\times9\times15}{3\times5\times12+6\times10\times24+9\times15\times36}\)

\(=\frac{1\times3\times5\times\left(1+2^3+3^3\right)}{3\times5\times12\times\left(1+2^3+3^3\right)}\)\(=\frac{1}{12}\)

=14535

5/3

= 1/3 : 1/5 = 1/3 x 5 = 5/3

5\3