D

D.f ( - 1 ) = - 23

HT

`(1/(1.3)+1/(3.5)+.......+1/(23.25))xx((x+1)+(x+3)+(x+5)+.....+(x+23))=144`

`(2/(1.3)+2/(3.5)+.......+2/(23.25))xx[(x+x+....+x)+(1+3+5+...+23)]=288`

`(1-1/3+1/3-1/5+.....+1/23-1/25)xx(12x+(24.12)/2)=288`

`(1-1/25)xx(12x+12.12)=288`

`24/25xx[12(x+12)]=288`

`24/25xx(x+12)=28`

`x+12=28:24/25=50`

`x=50-12=38`

Vậy `x=38`

\(=\dfrac{1}{2}-\left(\dfrac{1}{3\cdot7}+\dfrac{1}{7\cdot11}+...+\dfrac{1}{23\cdot27}\right)\)

\(=\dfrac{1}{2}-\dfrac{1}{4}\left(\dfrac{4}{3\cdot7}+\dfrac{4}{7\cdot11}+...+\dfrac{4}{23\cdot27}\right)\)

\(=\dfrac{1}{2}-\dfrac{1}{4}\left(\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{23}-\dfrac{1}{27}\right)\)

\(=\dfrac{1}{2}-\dfrac{1}{4}\cdot\dfrac{9-1}{27}\)

\(=\dfrac{1}{2}-\dfrac{1}{4}\cdot\dfrac{8}{27}=\dfrac{1}{2}-\dfrac{2}{27}=\dfrac{27-4}{54}=\dfrac{23}{54}\)

mày lười vừa phải thôi, có thế cũng hỏi

a) 23x51+75x23-23x25=23x(51+75-26)=23x100=2300

b) 1+2+3+...+20=\(\dfrac{\left(20+1\right)\text{x}20}{2}\)=210

a) \(23\times51+75\times23-23\times26\)

\(=23\times\left(51+75-26\right)\)

\(=23\times\left(126-26\right)\)

\(=23\times100\)

\(=2300\)

b) \(1+2+...+20\)

\(=\left(20+1\right)+\left(19+2\right)+\left(18+3\right)+\left(17+4\right)+...+\left(11+10\right)\)

\(=21+21+21+...+21\) (10 số 21)

\(=2100\) 

Sữa 210

1. Tính:

a) 23 + 24 - ( 65 x 2 - 4 ) x 4 + 66 + 44 - ( 54 : 9 x 9 : 9 + 45 ) : 1 + 1 - 1 x ( 23 + 23 - 23 x 2 +1 ) = 51

b) 4444444444444444444444444444444444444444444444444444444444444444444 : 1

= 4444444444444444444444444444444444444444444444444444444444444444444

c) 3⁰ = 0

d) 1/1 = 1

e)

a) - 530

b) 44444444444444444444444444444444444444444444444444444444444444444444

c) 0

d) 1

e) Em là em

-530

444444444444444444444444444444444444444444444444444444444444444

0

1

...

\(\dfrac{\dfrac{1}{3}+\dfrac{1}{7}-\dfrac{1}{23}}{\dfrac{2}{3}+\dfrac{2}{7}-\dfrac{2}{23}}\times\dfrac{\dfrac{1}{3}-0,25-0,2}{1\dfrac{1}{6}-0,875-0,7}\)

\(=\dfrac{\dfrac{1}{3}+\dfrac{1}{7}-\dfrac{1}{23}}{\dfrac{1}{3}+\dfrac{1}{3}+\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{23}-\dfrac{1}{23}}\times\dfrac{\dfrac{1}{3}-\dfrac{1}{4}-\dfrac{1}{5}}{\dfrac{7}{6}-\dfrac{7}{8}-\dfrac{7}{10}}\)

\(=\dfrac{\dfrac{1}{3} +\dfrac{1}{7}-\dfrac{1}{23}}{\dfrac{1}{3}\times2+\dfrac{1}{7}\times2-\dfrac{1}{23}\times2}\times\dfrac{\dfrac{2}{6}-\dfrac{2}{8}-\dfrac{2}{10}}{7\times\left(\dfrac{1}{6}-\dfrac{1}{8}-\dfrac{1}{10}\right)}\)

\(=\dfrac{\dfrac{1}{3}+\dfrac{1}{7}-\dfrac{1}{23}}{2\times\left(\dfrac{1}{3}+\dfrac{1}{7}-\dfrac{1}{23}\right)}\times\dfrac{2\times\left(\dfrac{1}{6}-\dfrac{1}{8}-\dfrac{1}{10}\right)}{7\times\left(\dfrac{1}{6}-\dfrac{1}{8}-\dfrac{1}{10}\right)}\)

\(=\dfrac{1}{2}\times\dfrac{2}{7}\)

\(=\dfrac{1}{7}\)

Ta có: \(23\dfrac{1}{4}:\left(-\dfrac{3}{7}\right)-23\dfrac{1}{4}:\left(-\dfrac{5}{7}\right)\)

\(=\dfrac{93}{4}\cdot\dfrac{-7}{3}-\dfrac{93}{4}\cdot\dfrac{-7}{5}\)

\(=\dfrac{93}{4}\cdot\left(-\dfrac{7}{3}+\dfrac{7}{5}\right)\)

\(=\dfrac{93}{4}\cdot\dfrac{-14}{15}=-\dfrac{217}{10}\)