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b: \(=12\left(35\cdot173+27\right)\)
\(=12\cdot6082=72984\)
321- 21. [(2.3^3+4^4 :32)]- 52
=321- 21. [(2.27+256 :32)]- 52
=321-21.[(54+8)]-52
=321-21.62-52
=321-1203-52
=-754
a: \(=23\cdot100+300=2600\)
b: \(=300:\left(4+6\right)-25=30-25=5\)
a) 100:{250:[450−(4.53−25.4)]}100:{250:[450−(4.53−25.4)]}
=100:{250:[450−(4.125−25.4)]}=100:{250:[450−(4.125−25.4)]}
=100:{250:[450−(500−100)]}=100:{250:[450−(500−100)]}
=100:[250:(450−400)]=100:[250:(450−400)]
=100:(250:50)=100:(250:50)
=100:5=100:5
=20=20
b) 4(18−15)−(5−3).324(18−15)−(5−3).32
=4.3−2.32=4.3−2.32
=4.3−2.9=4.3−2.9
=12−18=12−18
=−6=−6
\(=321-21\cdot\left[2\cdot27+256:32-52\right]\)
\(=321-21\cdot10=321-210=111\)
\(B=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+\frac{1}{18\cdot19\cdot20}\)
\(B=\frac{1}{2}\left(\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+\frac{2}{18\cdot19\cdot20}\right)\)
\(B=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+...+\frac{1}{18\cdot19}-\frac{1}{19\cdot20}\right)\)
\(B=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{19\cdot20}\right)\)
\(B=\frac{1}{2}\cdot\frac{189}{380}=\frac{189}{760}\)
\(C=\frac{52}{1\cdot6}+\frac{52}{6\cdot11}+\frac{52}{11\cdot16}+...+\frac{52}{31\cdot36}\)
\(C=\frac{52}{5}\left(\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+\frac{5}{11\cdot16}+...+\frac{6}{31\cdot36}\right)\)
\(C=\frac{52}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{31}-\frac{1}{36}\right)\)
\(C=\frac{52}{5}\cdot\left(1-\frac{1}{36}\right)\)
\(C=\frac{91}{9}\)
3: =231+26-209-26=22
4: =19(25+30+45)=19x100=1900
5: =-50+19+143+79-25-48
=-75+95+98
=98+20=118
\(73\cdot5^2+5^{28}-5^2\)
\(=72\cdot5^2+5^{28}\)
\(=5^2\left(5^{26}+72\right)\)