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\(S=2,5+\frac{23}{4}-\left(-3,75+\frac{1}{2}+\frac{13}{2}\right)\)
\(S=\frac{-25}{10}+\frac{23}{4}+3,75+\frac{1}{2}+\frac{13}{2}\)
\(S=\frac{-5}{2}+\frac{23}{4}+\frac{-375}{100}+\frac{1}{2}+\frac{13}{2}\)
\(S=\frac{-5}{2}+\frac{23}{4}+\frac{-15}{4}+\frac{1}{2}+\frac{13}{2}\)
\(S=\frac{-10}{4}+\frac{23}{4}+\frac{-15}{4}+\frac{2}{4}+\frac{26}{4}\)
\(S=\frac{26}{4}=\frac{13}{2}\)
\(12\frac{3}{11}-\frac{6}{13}+3,25-5\frac{3}{11}+\sqrt{1\frac{9}{16}}\)
\(=\frac{135}{11}-\frac{6}{13}+\frac{13}{4}-\frac{58}{11}+\sqrt{\frac{25}{16}}\)
\(=\frac{135}{11}-\frac{6}{13}+\frac{13}{4}-\frac{58}{11}+\frac{5}{4}\)
\(=\frac{135}{11}-\frac{58}{11}+\frac{13}{4}+\frac{5}{4}-\frac{6}{13}\)
\(=\frac{77}{11}+\frac{18}{4}-\frac{6}{13}\)
\(=7+\frac{9}{2}-\frac{6}{13}\)
\(=\frac{182}{26}+\frac{117}{26}-\frac{12}{26}\)
\(=\frac{287}{26}\)
a)\(23\frac{1}{4}\cdot\frac{7}{5}+13\frac{1}{4}\)/\(\frac{-5}{7}\)
=\(23\frac{1}{4}\cdot\frac{7}{5}+13\frac{1}{4}\cdot\frac{-7}{5}\)
=\(23\frac{1}{4}\cdot\frac{7}{5}+\left(-13\frac{1}{4}\right)\cdot\frac{7}{5}\)
=\(\frac{7}{5}\cdot\left(23\frac{1}{4}-13\frac{1}{4}\right)\)
=\(\frac{7}{5}\cdot\left(23-13+\frac{1}{4}-\frac{1}{4}\right)\)
=\(\frac{7}{5}\cdot10\)
=\(14\)
b)\(\left(-3\right)^2\cdot\left(\frac{3}{4}-0.25\right)-\left(3\frac{1}{2}-1\frac{1}{2}\right)\)
=\(9\cdot\left(\frac{3}{4}-\frac{1}{4}\right)-\left(3-1+\frac{1}{2}-\frac{1}{2}\right)\)
=\(9\cdot\frac{1}{2}-2\)
=\(\frac{9}{2}-2\)
=\(\frac{9}{2}-\frac{4}{2}\)
=\(\frac{5}{2}\)
Nếu mình còn sai hay thiếu chỗ nào thì ae bảo mình nha :))
ta có
S=1+ 1/2 +1/2^2 +..+1/2^100
=> S/2 -S=1/2+ 1/2^2+...+1/2^101-1-1/2-...1/2^100
=> -S/2=1/2^101-1
=> -S/2=(1-2^101)/2^101
=> S=-2*(1-2^101)/2^101
=> S=(2^101-1)/2^100
e) \(\frac{1}{7}.\frac{-3}{8}+\frac{-13}{8}.\frac{1}{7}\)
\(=\frac{1}{7}.\left[\left(-\frac{3}{8}\right)+\left(-\frac{13}{8}\right)\right]\)
\(=\frac{1}{7}.\left(-2\right)\)
\(=-\frac{2}{7}.\)
Chúc bạn học tốt!
Câu 2: Ta có \(S=6^2+18^2+30^2+...+126^2\)
\(S=6^2\left(1^2+3^2+5^2+...+21^2\right)\)
\(=6^2.1771=36.1771=63756\)
a) \(\frac{11}{24}-\frac{5}{41}+\frac{13}{24}+0,5-\frac{36}{41}\)
= \(\frac{11}{24}-\frac{5}{41}+\frac{13}{24}+\frac{1}{2}-\frac{36}{41}\)
= \(\frac{1}{2}-\left\{\frac{11}{24}+\frac{13}{24}\right\}-\left\{\frac{5}{41}+\frac{36}{41}\right\}\)
=\(\frac{1}{2}-\frac{24}{24}-\frac{41}{41}\)
=\(\frac{1}{2}-1-1\)
=\(\frac{-3}{2}\)
b) \(-12:\left\{\frac{3}{4}-\frac{5}{6}\right\}^2\)
= \(-12:\left\{\frac{9}{12}-\frac{10}{12}\right\}^2\)
= \(-12:\left\{\frac{-1}{12}\right\}^2\)
= \(-12:\frac{1}{144}\)
= \(-12.144\)
= -1728
c) \(\frac{7}{23}.\left[\left(\frac{-8}{6}\right)-\frac{45}{18}\right]\)
= \(\frac{7}{23}.\left[\left(\frac{-24}{18}\right)-\frac{45}{18}\right]\)
= \(\frac{7}{23}.\left(\frac{-23}{6}\right)\)
= \(\frac{-7}{6}\)
d) \(23\frac{1}{4}.\frac{7}{5}-13\frac{1}{4}:\frac{5}{7}\)
= \(23\frac{1}{4}.\frac{7}{5}-13\frac{1}{4}.\frac{7}{5}\)
= \(\left\{23\frac{1}{4}-13\frac{1}{4}\right\}.\frac{7}{5}\)
= \(10.\frac{7}{5}\)
= 14
e) (1+23−14).(0,8−34)2
= (1+23−14).(\(\frac{4}{5}\)−34)2
= \(\left(\frac{12}{12}+\frac{8}{12}-\frac{3}{12}\right).\left(\frac{16}{20}-\frac{15}{20}\right)^2\)
= \(\frac{17}{12}.\left(\frac{1}{20}\right)^2\)
= \(\frac{17}{20}.\frac{1}{400}\)
= \(\frac{17}{8000}\)
\(S=-2,5+\frac{23}{4}-\left(-3,25+\frac{1}{2}+\frac{13}{2}\right)\)
\(S=-\frac{5}{2}+\frac{23}{4}-\left(-\frac{13}{4}+\frac{1}{2}+\frac{13}{2}\right)\)
\(S=-\frac{5}{2}+\frac{23}{4}-\left(\frac{15}{4}\right)\)
\(S=-\frac{1}{2}\)
\(S=-2,5+\frac{23}{4}-\left(-3,25+\frac{1}{2}+\frac{13}{2}\right)\)
\(S=-2,5+\frac{23}{4}+3,25-\frac{1}{2}-\frac{13}{2}\)
\(S=\frac{23}{4}-2,5+3,25-7\)
\(S=3,25+3,25-7\)
\(S=6,5-7\)
\(S=-0,5\)