\(\frac{3}{5.22}+\frac{54}{44.65}+\frac{18}{65.72}=\frac{3}{110}+\frac{54}{2860}+\frac{18}{4680}=\frac{3}{65}+\frac{1}{260}=\frac{1}{20}\)

\(\frac{\frac{3}{67}.\left(17\frac{21}{56}-13\frac{21}{45}\right):\left(\frac{3}{5.22}+\frac{54}{44.65}+\frac{18}{65.72}\right)}{29^3:100-29^3:0,47}\)

\(=\frac{\frac{3}{67}\left(\frac{139}{8}-\frac{202}{15}\right):\left(\frac{3}{110}+\frac{54}{2860}+\frac{18}{4680}\right)}{29^3.\frac{1}{100}-29^3.\frac{47}{100}}\)

\(=\frac{\frac{3}{67}.\frac{469}{120}:\frac{1}{20}}{29^3\left(\frac{1}{100}-\frac{47}{100}\right)}\)

\(=\frac{\frac{7}{40}.20}{29^3.\left(-\frac{23}{50}\right)}\).

\(=\frac{\frac{7}{2}}{-11218,94}\)

\(=-\frac{175}{560947}\)

arigato gozaimasu

\(\frac{1}{3}-\left(\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+\frac{1}{180}+\frac{1}{270}+\frac{1}{378}\right)\)

\(=\frac{1}{3}-\left(\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+\frac{1}{12.15}+\frac{1}{15.18}+\frac{1}{18.21}\right)\)

\(=\frac{1}{3}-\left(\frac{1}{3}-\frac{1}{21}\right)\)

\(=\frac{1}{3}-\frac{1}{3}+\frac{1}{21}=\frac{1}{21}\)

Đáp án là : \(\frac{5}{21}\)

3H = 3 (1/3-1/8-1/54-1/108-1/180-1/270-1/378) 
3H+(3/8) = 3/3 - 3/(6x9) - 3/(9x12) - 3/(12x15) - 3/(15x18) - 3/(1/18x21) 
3H+(3/8) = 1 - [(1/6)-(1/9)] - [(1/9)-(1/12)] - [(1/12)-(1/15)] - [(1/15)-(1/18)] - [(1/18)-(1/21)] 
= 1 -1/6 +1/9 -1/9 +1/12 -1/12 +1/15 -1/15 +1/18 -1/18 +1/21 
3H = -(3/8) + 1 -(1/6) +(1/21) 
3H = (-63 +168 -28 +8) / 168 
3H = 85/168 
đáp số: 
H = 85/504 
gần bằng 0,17