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a) 50+3x(25-16)2+150
=50+3x92+1
=50+3x81+1
=50+243+1
=294
b)22x52-35/32
=(2x5)2-35-2
=102-33
=100-27
=73
c)80-[130-(12-4)2 ]
=80-[130-82 ]
=80-[130-64]
=80-66
=14
d)100:[2x(52-35-8)]
=100:[2x9]
=100:18
=100/18
e)24:{300:[375-(150+15x5)]}
=24:{300:[375-(150+75)]}
=24:{300:[375-225]}
=24:{300:50}
=24:6
=4
\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{99}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{100}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{99}+\frac{1}{100}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{100}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{50}\right)=\frac{1}{51}+\frac{1}{52}+...+\frac{1}{100}\)
\(\RightarrowĐPCM\)