a) 11-12+13-14+15-16+17-18+19-20

= -1 + ( -1 )+ ( -1 )+ ( -1 )+ ( -1 )

= -1 . 5

= -5

b) 101-102-(-103)-104-(105)-106-(107)-108-(-109)-110

= -1 + ( -1 )+ ( -1 )+ ( -1 )+ ( -1 )

= -1 . 5

= -5

a) \(\left(6-\frac{2}{3}+\frac{1}{2}\right)\)- \(\left(5+\frac{5}{3}-\frac{2}{3}\right)\)- \(\left(3-\frac{7}{3}+\frac{5}{2}\right)\)

= \(6-\frac{2}{3}+\frac{1}{2}-5-\frac{5}{3}+\frac{2}{3}-3+\frac{7}{3}-\frac{5}{2}\)

= \(-2+\frac{2}{3}-\frac{4}{2}\)

= \(\frac{-12}{6}+\frac{4}{6}-\frac{12}{6}\)= \(\frac{4}{6}=\frac{2}{3}\)

a/\(\left(6-\frac{2}{3}+\frac{1}{2}\right)-\left(5+\frac{5}{3}-\frac{2}{3}\right)-\left(3-\frac{7}{3}+\frac{5}{2}\right)..\)

\(=\left(6-\frac{1}{6}\right)-\left(5+1\right)-\left(3-\frac{-1}{6}\right)\)

\(=6-\frac{1}{6}-\left(5+1\right)-3-\frac{1}{6}\)

\(=\left[6-\left(5+1\right)\right]-\frac{1}{6}-\frac{1}{6}-3\)

\(=0-\frac{1}{6}-\frac{1}{6}-3\)

\(=\frac{-1}{6}-\frac{1}{6}-3\)

\(=\frac{-10}{3}\)

\(\left(\frac{-1}{\frac{1}{2}}:1,25\right)+\left(\frac{10}{\frac{3}{7}}:\frac{5}{\frac{3}{14}}\right)\)

\(=\left(-2:1,25\right)+\left(\frac{70}{3}:\frac{70}{3}\right)\)

\(=\frac{-8}{5}+1=\frac{-3}{5}\)

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\(c=2^3.5^3-\left\{7^2.2^3-5^2.\left[4^3::8+11^2:121-2\left(37-5.7\right)\right]\right\}\)

\(c=8.5-\left\{49.8-25.\left[8:8+121:121-2\left(37-5.7\right)\right]\right\}\)

\(c=8.5-\left\{49.8-25.\left[8:8+121:121-2\left(37-35\right)\right]\right\}\)

\(c=8.5-\left\{49.8-25.\left[8:8+121:121+2.2\right]\right\}\)

\(c=8.5-\left\{1+1+2.2\right\}\)

\(c=8.5-\left\{1+1+4\right\}\)

\(c=8.5-6\)

\(c=40-6\)

\(c=34\)

nhầm

\(c=2^3.5^3-\left\{7^2.2^3-5^2.\left[4^3:8+11^2:121-2\left(37-5.7\right)\right]\right\}\)

\(c=8.125-\left\{49.8-25.\left[8:8+121:121-2\left(37-35\right)\right]\right\}\)

\(c=8.125-\left\{49.8-25.\left[8:8+121:121-2.2\right]\right\}\)

\(c=8.125-\left\{49.8-25.\left[1+1-2.2\right]\right\}\)

\(c=8.125-\left\{49.8-25.\left[1+1-4\right]\right\}\)

\(c=8.125-\left\{49.8-25.-2\right\}\)

\(c=8.125-\left\{392+50\right\}\)

\(c=8.125-442\)

\(c=1000-442\)

\(c=558\)

a.
\(1500-\left\{5^3.2^3-11\left[7^2-5.2^3+8\cdot\left(11^2-121\right)\right]\right\}\)
\(=1500-\left\{\left(5.2\right)^3-11\left[9+8\left(11^2-11^2\right)\right]\right\}\)
\(=1500-\left\{10^3-11.9\right\}\)
\(=1500-901=599\)
b/
\(S=5+5^2+5^3+...+5^{2012}\)
\(5S=5^2+5^3+5^4+...+5^{2013}\)
\(4S=5S-S=5^{2013}-5\)
\(S=\frac{5^{2013}-5}{4}\)

a ; 1500 - { 5 ^ 3 . 2 ^ 3 - 11 [ 7 ^ 2 - 5 . 2 ^ 3 + 8 ( 11 ^ 2 - 121) ] }

a ; 1500 - { 5 ^ 3 . 2 ^ 3 - 11 [ 7 ^ 2 - 5 . 2 ^ 3 + 8 ( 121    - 121) ] }

a ; 1500 - [ 5 ^ 3 . 2 ^ 3 - 11 ( 7 ^ 2 - 5 . 2 ^ 3 + 8 . 0 ) ]

a ; 1500 - [ 5 ^ 3 . 2 ^ 3 - 11 ( 49 - 5 .8 + 8 . 0) ]

a ; 1500 - [ 5 ^ 3 . 2 ^ 3 - 11 ( 49 -   40 +   0   ) ]

a ; 1500 - ( 5 ^ 3 . 2 ^ 3 - 11 .              9         )

a ; 1500 - [ ( 5 . 2 ) ^ 3 - 99]

a ; 1500 - ( 10 ^ 3 - 99)

a ; 1500 - (  1000 - 99)

a ; 1500 - 901

a = 599

1500- { 5³ . 2³- 11. [ 7² - 5 . 2³ + 8.( 11² - 121)]}

=1500- { 5³ . 2³- 11. [ 7² - 5 . 2³ + 8.( 121 - 121)]}

=1500- { 5³ . 2³- 11. [ 7² - 5 . 2³ + 8.0 ]}

=1500- { 5³ . 2³- 11. [ 49 - 5 . 8 + 0 ]}

=1500- { 5³ . 2³- 11. [ 49 - 40 + 0 ]}

=1500- { 5³ . 2³- 11. [ 9 + 0 ]}

=1500- { 5³ . 2³- 11. 9 }

=1500- { 125 . 8 - 11. 9 }

=1500- { 1000 - 99 }

=1500- 901

=599

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