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28,37-23,18-16,82+71,63
=(28,37+71,63)-(23,18+16,82)
=60
B=1/1x6 + 1/6x11 + 1/16x21 + 1/21x26 + 1/26x31
=1-1/6+1/6-1/11+1/11-....-1/31
=1-1/31=30/31
a) A = \(\left(28,37+71,63\right)-\left(23,18+16,82\right)\)
= 100 - 40
= 60
b) \(B=\dfrac{1}{1.6}+\dfrac{1}{6.11}+\dfrac{1}{11.16}+\dfrac{1}{16.21}+\dfrac{1}{21.26}+\dfrac{1}{26.31}\)
= \(\dfrac{1}{5}\left(\dfrac{5}{1.6}+\dfrac{5}{6.11}+...+\dfrac{5}{26.31}\right)\)
= \(\dfrac{1}{5}\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{26}-\dfrac{1}{31}\right)\)
= \(\dfrac{1}{5}\left(1-\dfrac{1}{31}\right)=\dfrac{1}{5}.\dfrac{30}{31}=\dfrac{6}{31}\)
\(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\)
\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}\)
\(=\dfrac{1}{2}-\dfrac{1}{6}\)
\(=\dfrac{1}{3}\)
\(\dfrac{1}{4}\) : 0,25 - \(\dfrac{1}{8}\) : 0,125 + \(\dfrac{1}{2}\) : 0,5 - 1
= 0,25 x 4 - 0,125 x 8 + 0,5 x 2 - 1
= 1 - 1 + 1 - 1
= 0 + 1 - 1
= 1 - 1
= 0
A = \(\dfrac{1}{4}\) : 0,25 - \(\dfrac{1}{8}\): 0,125 + \(\dfrac{1}{2}\): 0,5 - 1
A = \(\dfrac{1}{4}\) x 4 - \(\dfrac{1}{8}\) x 8 + \(\dfrac{1}{2}\) x 2 - 1
A = 1 - 1 + 1 - 1
A = (1 - 1) + (1 - 1)
A = 0
\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+....+\dfrac{1}{110}\)
\(=\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+....+\dfrac{1}{10\times11}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+....+\dfrac{1}{10}-\dfrac{1}{11}\)
\(=1-\dfrac{1}{11}=\dfrac{10}{11}\)
\(\dfrac{1}{10}+\dfrac{1}{2}:0,5-\dfrac{1}{4}:0,25+\dfrac{1}{8}:0,125\)
\(=\dfrac{1}{10}+\dfrac{1}{2}\times2-\dfrac{1}{4}\times4+\dfrac{1}{8}\times8\)
\(=\dfrac{1}{10}+1-1+1\)
\(=\dfrac{1}{10}+1=\dfrac{1}{10}+\dfrac{10}{10}=\dfrac{11}{10}\)
\(\left(1-\dfrac{1}{2}\right)\times\left(1-\dfrac{1}{3}\right)\times\left(1-\dfrac{1}{4}\right)\times\left(1-\dfrac{1}{6}\right)\times\left(1-\dfrac{1}{6}\right)\)
\(=\dfrac{1}{2}\times\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{4}{5}\times\dfrac{5}{6}\)
\(=\dfrac{1\times2\times3\times4\times5}{2\times3\times4\times5\times6}\)
\(=\dfrac{1}{6}\)
\(\left(1-\dfrac{1}{4}\right)\times\left(1-\dfrac{1}{9}\right)\times...\times\left(1-\dfrac{1}{576}\right)\times\left(1-\dfrac{1}{625}\right)\)
\(=\dfrac{3}{4}\times\dfrac{8}{9}\times\dfrac{15}{16}\times...\times\dfrac{575}{576}\times\dfrac{624}{625}\)
\(=\left(\dfrac{3}{2}\times2\right)\times\left(\dfrac{8}{3}\times3\right)\times\left(\dfrac{15}{4}\times4\right)...\times\left(\dfrac{575}{24}\times24\right)\times\left(\dfrac{624}{25}\times25\right)\)
\(=\dfrac{1\times3\times2\times4\times3\times5\times...\times23\times25\times24\times26}{2\times3\times4\times...\times25\times2\times3\times4\times...\times25}\)
\(=\dfrac{1\times2\times3\times4\times...\times24\times3\times4\times...\times26}{2\times3\times4\times...\times25\times2\times3\times4\times...\times25}\)
\(=\dfrac{1\times26}{2\times25}=\dfrac{26}{50}=\dfrac{13}{25}=0,52\)
=(1-1/2)(1-1/3)*...*(1-1/25)(1+1/2)(1+1/3)*...*(1+1/25)
=1/2*2/3*...*24/25*3/2*4/3*...*26/25
=1/25*26/2
=26/50=13/25