\(\frac{4}{3}B=-1+\frac{3}{4}-\left(\frac{3}{4}\right)^2+...+\left(\frac{3}{4}\right)^{99}\)

\(B=-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+...+\left(\frac{3}{4}\right)^{100}\)

\(\Rightarrow\)\(\frac{7}{3}B=-1+\left(\frac{3}{4}\right)^{100}\Rightarrow B=\frac{\left(\frac{3}{4}\right)^{100}-1}{\frac{7}{3}}=\frac{3\left[\left(\frac{3}{4}\right)^{100}-1\right]}{7}\)

Như vầy đủ gọn chưa bạn?

\(\frac{3}{4.7}=\frac{1}{4}-\frac{1}{7}\); \(\frac{1}{7.8}=\frac{1}{7}-\frac{1}{8}\); \(\frac{5}{8.13}=\frac{1}{8}-\frac{1}{13}\); \(\frac{2}{13.15}=\frac{1}{13}-\frac{1}{15}\); \(\frac{9}{15.24}=\frac{1}{15}-\frac{1}{24}\)

nên ta được tổng trên là : \(\frac{1}{4}-\frac{1}{7}\)\(+\frac{1}{7}-\frac{1}{8}\)\(+\frac{1}{8}-\frac{1}{13}\)\(+\frac{1}{13}-\frac{1}{15}\)\(+\frac{1}{15}-\frac{1}{24}\)= \(\frac{1}{4}-\frac{1}{24}\)= 5/24

Nấu bạn k cho mình lên 3 điểm hỏi đáp thì mình sẽ giúp

cảm ơn bạn nha

\(\left(\frac{14}{5}x-50\right)\div\frac{2}{3}=51\)

\(\Leftrightarrow\frac{14}{5}x-50=51\times\frac{2}{3}\)

\(\Leftrightarrow\frac{14}{5}x-50=34\)

\(\Leftrightarrow\frac{14}{5}x=34+50\)

\(\Leftrightarrow\frac{14}{5}x=84\)

\(\Leftrightarrow x=84\div\frac{14}{5}\)

\(\Leftrightarrow x=84\times\frac{5}{14}\)

\(\Leftrightarrow x=30\)

\(\left(\frac{14}{5}.x-50\right):\frac{2}{3}=51\)

\(\frac{14}{5}.x-50=51.\frac{2}{3}\)

\(\frac{14}{5}.x-50=34\)

\(\frac{14}{5}.x=34+50\)

\(\frac{14}{5}.x=84\)

\(x=84:\frac{14}{5}\)

\(x=30\)

( 14/5 . x - 50 ) : 2/3 = 51

14/5 . x - 50 = 51 . 2/3

14/5 .x - 50 = 34

14/5.x = 34 + 50

14/5.x = 84

=> x = 30

-5 x ( x + 1/5 ) - 1/2 x ( x - 2/3 ) = 3/2x - 5/6

<=> -5x^2 - x - 1/2 x^2 + 1/3 = 3/2x - 5/6

<=> -3x^2 - x + 1/3 = 3/2x - 5/6

<=> -3x^2  - 5/2 x + 7/6 = 0

<=> ( 3x - 1 ) ( 6x + 7 ) = 0

=> x = 1/3 ; x = -7/6 .

Vậy x = 1/3 , x = -7/6.

\(78-\left(x-25\right).3\frac{1}{3}=73\)

\(78-\left(x-25\right)\cdot\frac{10}{3}=73\)

\(\left(x-25\right)\cdot\frac{10}{3}=78-73\)

\(\left(x-25\right)\cdot\frac{10}{3}=5\)

\(x-25=5:\frac{10}{3}\)

\(x-25=1,5\)

\(x=25+1,5=26,5\)

19x64+76x34

=(19x4)x16+76x34

=76x(16+34)

=76x50

=3800

a) 19 x 64 + 76 x 34

= 19 x 64 + 19 x 4 x 34

= 19 x ( 64 + 4 x 34 )

= 19 x 200

= 3800

k cho mình rùi mình giải bài b) cho

\(\frac{x}{2}-\frac{11}{5}=\frac{7}{5}.\frac{64}{49}\)

\(\frac{x}{2}-\frac{11}{5}=\frac{64}{35}\)

\(\frac{x}{2}=\frac{64}{35}+\frac{11}{5}\)

\(\frac{x}{2}=\frac{141}{35}\)

\(\Leftrightarrow x.35=2.141\)

\(\Leftrightarrow x.35=282\)

\(\Leftrightarrow x=282:35\)

\(\Leftrightarrow x=\frac{282}{35}\)

x/2 - 11/5 = 7/5.64/49

=> x/2 - 11/5 = 64/35

=> x/2 = 64/35 + 11/5

=> x/2 = 141/35

=> 35x = 2.141

=> 35x = 282

=> x = 282 : 35 = 282/35

12x+3.2³=2³.x-4.3²

12x+3.8=8.x-4.9

12x+24=8x-36

12x-8x=36-24

4x=12

x=12:4=3

      \(12x+3\cdot2^3=2^3x-4\cdot3^2\)

\(\Rightarrow12x+24=8x-36\)

\(\Rightarrow12x-8x=-36-24\)

\(\Rightarrow4x=-60\)

\(\Rightarrow x=-15\)

Vay x=-15

k mk nhA