\(D=\frac{1}{2}-\frac{1}{2^4}+\frac{1}{2^7}-\frac{1}{2^{10}}+...+\frac{1}{2^{55}}-\frac{1}{2^{58}}\)

\(\Rightarrow2^3D=2^2-\frac{1}{2}+\frac{1}{2^4}-\frac{1}{2^7}+....+\frac{1}{2^{52}}-\frac{1}{2^{55}}\)

\(\Rightarrow8D+D=2^2-\frac{1}{2^{58}}\)

\(\Rightarrow D=\frac{2^2-\frac{1}{2^{58}}}{9}\)

\(\frac{1}{2^3}\)D= \(\frac{1}{2^4}-\frac{1}{2^7}+\frac{1}{2^{10}}-\frac{1}{2^{13}}+...+\frac{1}{2^{58}}-\frac{1}{2^{61}}\)

D+ \(\frac{1}{2^3}\)D=\(\frac{1}{2}-\frac{1}{2^4}+\frac{1}{2^4}+\frac{1}{2^7}-\frac{1}{2^7}-\frac{1}{2^{10}}+\frac{1}{2^{10}}+...-\frac{1}{2^{58}}+\frac{1}{2^{58}}-\frac{1}{2^{61}}\)

\(\frac{9}{8}\)D= \(\frac{1}{2}-\frac{1}{2^{61}}\)=> D= \(\frac{\frac{1}{2}-\frac{1}{2^{61}}}{\frac{9}{8}}\)

C = 1/3 + -3/4 + 3/5 + 1/57 + -1/36 + 1/15 + -2/9

C = ( 1/3 + 1/57 ) + ( -3/4 + -1/36 ) + ( 3/5 + 1/15 ) + -2/9 

C = ( 19/57 + 1/57 ) + ( -27/36 + -1/36 ) + ( 9/15 + 1/15 ) + -2/9 

C = 20/57 + -28/36 + 10/15 + -2/9 

C = 20/57 + -7/9 + 2/3 + -2/9

C = ( 20/57 + 2/3 ) + ( -7/9 + -2/9 )

C = 58/57 + -1 

C = 1/57

D = 1/2 + -1/5 + -5/7 + 1/6 + -3/35 + 1/3 + 1/41

D = ( 1/2 + 1/3 + 1/6 ) + ( -1/5 + -5/7 +-3/35 ) + 1/41

D = ( 3/6 + 2/6 + 1/6 ) + ( -7/35 + -25/35 + -3/35 ) + 1/41

D = 1 + -1 + 1/41

D = 1/41

E = -1/2 + 3/5 + -1/9 + 1/127 + -7/18 + 4/35 + 2/7 

E = ( -1/2 + -1/9 + -7/18 ) + ( 3/5 + 4/35 ) + 1/127 + 2/7

E = ( -9/18 + -2/18 + -7/18 ) + ( 21/35 + 4/35 ) + 1/127 + 2/7

E = -1 + 5/7 + 1/257 + 2/7 

E = -1 + ( 5/7 + 2/7 ) + 1/127

E = -1 + 1 + 1/127

E = 1/127

\(C=\frac{1}{3}+\frac{-3}{4}+\frac{3}{5}+\frac{1}{57}+\frac{-1}{36}+\frac{1}{15}+\frac{-2}{9}.\)

\(C=\left(\frac{1}{3}+\frac{3}{5}+\frac{1}{15}\right)-\left(\frac{3}{4}+\frac{1}{36}+\frac{2}{9}\right)+\frac{1}{57}\)

\(C=1-1+\frac{1}{57}\)

\(C=\frac{1}{57}\)

D=1/2+-1/5+-5/7+1/6+-3/35+1/3+1/41

D=(1/2+1/6+1/3)-(1/5+3/35+5/7)+1/41

D=1-1+1/41

D=1/41

E=-1/2+3/5+-1/9+1/127+-7/18+4/35+2/7

E=(3/5+4/35+2/7)-(1/2+1/9+7/18)+1/127

E=1-1+1/127

E=1/127

tae tae ơi khó quá hổng hiểu j hết trơn

mình làm câu cuối thôi nhé , những câu còn lại bạn tự làm đi , dễ mà :)))) chỉ cần quy đồng mẫu lên là được 

\(=\frac{x+1}{58}+1+\frac{x+2}{57}+1=\frac{x+3}{56}+1+\frac{x+4}{55}\)

\(=\frac{x+59}{58}+\frac{x+59}{57}=\frac{x+59}{56}+\frac{x+59}{55}\)

\(=\frac{x+59}{58}+\frac{x+59}{57}-\frac{x+59}{56}-\frac{x+59}{55}=0\)

\(=\left(x+59\right)\left(\frac{1}{58}+\frac{1}{57}-\frac{1}{56}-\frac{1}{55}\right)=0\)

Vì \(\left(\frac{1}{58}+\frac{1}{57}-\frac{1}{56}-\frac{1}{55}\right)\) luôn khác 0 

<=> x + 59 = 0 

<=> x=-59 

D=1/2-1/2⁴ +1/2⁷-1/2¹⁰ +.......+1/2⁵⁸

2D =1 - 1/2-1/2⁴ +1/2⁷-1/2¹⁰ +.......+1/2⁵⁷

2D -D =(1 - 1/2-1/2⁴ +1/2⁷-1/2¹⁰ +.......+1/2⁵⁷)-(1/2-1/2⁴ +1/2⁷-1/2¹⁰ +.......+1/2⁵⁸)

D=1-1/2⁵⁸

a) 20,7 + 1,47 : 7 - 0,23 . 5

= 20,7 + 0,21 – 1,15

= 20,91 – 1,15

= 19,76

Ở trên vietjack có đó bn =)

a, 20,7 + 1,47 : 7 - 0,23 . 5

=\(\frac{207}{10}+\frac{147}{100}:7-\frac{23}{100}.5\)

= \(\frac{207}{10}+\frac{21}{100}-\frac{23}{20}\)

= \(\frac{2091}{100}+\frac{-23}{20}\)

= \(\frac{494}{25}\)

\(a,20,7+1,47:7-0,23\cdot5\)

\(=20,7+0,21-1,15=19,76\)

\(b,1\frac{4}{5}\cdot\frac{7}{8}+\frac{4}{29}:\frac{5}{58}-1\frac{3}{10}\)

\(=\frac{9}{5}\cdot\frac{7}{8}+\frac{4}{29}:\frac{5}{58}-\frac{13}{10}\)

\(=\frac{9\cdot7}{5\cdot8}+\frac{4}{29}\cdot\frac{58}{5}-\frac{13}{10}\)

\(=\frac{63}{40}+\frac{4}{1}\cdot\frac{2}{5}-\frac{13}{10}\)

\(=\frac{63}{40}+\frac{8}{5}-\frac{13}{10}=\frac{63}{40}+\frac{64}{40}-\frac{52}{40}=\frac{63+64-52}{40}=\frac{75}{40}=\frac{15}{8}\)