\(\frac{3}{2}\)+\(\frac{1}{3}+\frac{3}{4}\)
trình bày ra
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1-1/2+2-2/3+3/4+4-1/4-3-1/3-2-1/2-1=(1-2+4-3-3-3)(1/2-2/3+3/4-1/4-1/3-1/2)=-6.(-1/6)=1
Ta có: \(1-\frac{1}{2}+2-\frac{2}{3}+\frac{3}{4}+4-\frac{1}{4}-3-\frac{1}{3}-2-\frac{1}{2}\)\(-1\)
\(=\left(1+2+4-3-2-1\right)+\left(-\frac{1}{2}-\frac{2}{3}+\frac{3}{4}-\frac{1}{4}-\frac{1}{3}-\frac{1}{2}\right)\)
\(=1+\left(\frac{-3}{2}\right)\)
\(=\frac{-1}{2}\)
ở tử số ta làm thế này
\(TS=\left(1+\frac{1}{2014}\right)+\left(1+\frac{1}{2013}\right)+\left(1+\frac{1}{2012}\right)+...+\left(1+\frac{2013}{2}\right)\)
\(TS=2015\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}+...+\frac{1}{2}\right)\)
\(\frac{TS}{MS}=2015\)
999 - 888 - 111 + 111 - 111 + 111 - 111
= 111 - 111 + 111 - 111 + 111 - 111
= 0 + 111 - 111 + 111 - 111
= 111 - 111 + 111 - 111
= 0 + 111 - 111
= 111 - 111
= 0
=\(\frac{3\left(\frac{1}{1}-\frac{1}{11}+\frac{1}{13}\right)}{5\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}+\frac{\frac{2}{4}+\frac{2}{6}+\frac{2}{8}}{5\left(\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\right)}\)
=\(\frac{3}{5}+\frac{2\left(\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\right)}{5\left(\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\right)}\)=\(\frac{3}{5}+\frac{2}{5}=\frac{5}{5}=1\)
A=\(\frac{1}{3}-\frac{3}{5}+\frac{5}{7}-\frac{7}{9}+\frac{9}{11}-\frac{11}{13}-\frac{9}{11}+\frac{7}{9}-\frac{5}{7}+\frac{3}{5}-\frac{1}{3}\)
A=[ \(\frac{1}{3}-\frac{1}{3}\)] + [ \(-\frac{3}{5}+\frac{3}{5}\)] + [ \(-\frac{5}{7}+\frac{5}{7}\)] + [ \(-\frac{7}{9}+\frac{7}{9}\)] + [ \(-\frac{9}{11}+\frac{9}{11}\)] \(-\frac{11}{13}\)
Các bạn tự làm tiếp nhé!Sorry
\(C=\left(\frac{1}{2^2}-1\right)\left(\frac{1}{3^2}-1\right)\left(\frac{1}{4^2}-1\right)...\left(\frac{1}{100^2}-1\right)\)
\(C=\frac{2^2-1}{2^2}.\frac{3^2-1}{3^2}.\frac{4^2-1}{4^2}...\frac{100^2-1}{100^2}\)
\(C=\frac{\left(2-1\right)\left(2+1\right)}{2^2}.\frac{\left(3-1\right).\left(3+1\right)}{3^2}.\frac{\left(4-1\right)\left(4+1\right)}{4^2}...\frac{\left(100-1\right)\left(100+1\right)}{100^2}\)
\(C=\frac{1.3}{2^2}.\frac{2.4}{3^2}.\frac{3.5}{4^2}...\frac{99.101}{100^2}\)
\(C=\frac{2.3^2.4^2.5^2...99^2.100.101}{2^2.3^2.4^2...100^2}\)
\(C=\frac{101}{200}\)
\(\frac{3}{2}+\frac{1}{3}+\frac{3}{4}\)
\(=\frac{18}{12}+\frac{4}{12}+\frac{9}{12}\)
\(=\frac{31}{12}\)
_HT_
TL :
\(\frac{3}{2}\)\(+\frac{1}{3}\)\(+\frac{3}{4}\)
\(=\left(\frac{3}{2}+\frac{3}{4}\right)+\frac{1}{3}\)
\(=\frac{9}{4}\)\(+\frac{1}{3}\)
\(=\frac{31}{12}\)