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1+2+3+4+5+6+7+8+9+10
=(1+10)+(2+9)+(3+8)+(4+7)+(5+6)
=11+11+11+11+11
=11x5
=55
#)Giải :
\(\frac{1}{11}+\frac{2}{11}+\frac{3}{11}+\frac{4}{11}+\frac{5}{11}+\frac{6}{11}+\frac{7}{11}+\frac{8}{11}+\frac{9}{11}+\frac{10}{11}\)
\(=\left(\frac{1}{11}+\frac{10}{11}\right)+\left(\frac{2}{11}+\frac{9}{11}\right)+\left(\frac{3}{11}+\frac{8}{11}\right)+\left(\frac{4}{11}+\frac{7}{11}\right)+\left(\frac{5}{11}+\frac{6}{11}\right)\)
\(=1+1+1+1+1\)
\(=5\)
#~Will~be~Pens~#
\(\frac{2}{3}+\frac{2007}{2009}+\frac{4}{3}-1\)
\(=\frac{2}{3}+\frac{4}{3}+\frac{2007}{2009}-1\)
\(=2+\frac{-2}{2009}\)
\(=\frac{4018}{2009}-\frac{2}{2009}\)
\(=\frac{4016}{2009}\)
Học tốt
\(C1:\left(\frac{1}{3}+\frac{1}{5}\right)x\frac{1}{2}\)
\(=\left(\frac{5}{15}+\frac{3}{15}\right)x\frac{1}{2}\)
\(=\frac{8}{15}x\frac{1}{2}\)
\(=\frac{4}{15}\)
~ Học tốt ~
\(C2:(\frac{1}{3}+\frac{1}{5})x\frac{1}{2}\)
\(=\frac{1}{2}x\frac{1}{3}+\frac{1}{2}x\frac{1}{5}\)
\(=\frac{1}{6}+\frac{1}{10}\)
\(=\frac{3}{30}+\frac{5}{30}\)
\(=\frac{8}{30}=\frac{4}{15}\)
~ Học tốt ~
\(\frac{4}{7}-\frac{1}{3}< \frac{1}{2}-\frac{2}{9}\)
\(\frac{125}{100}-\frac{48}{64}< \frac{6}{7}-\frac{14}{28}\)
\(\frac{7}{5}-\frac{20}{25}=\frac{1}{5}+\frac{4}{10}\)
\(\frac{45}{75}+\frac{22}{33}>\frac{4}{5}+\frac{4}{6}\)
#H
\(\frac{1}{2}+\frac{1}{2}+\frac{3}{4}+\frac{5}{10}+\frac{4}{6}+\frac{5}{20}\)
\(=\frac{1}{2}+\frac{1}{2}+\frac{3}{4}+\frac{1}{2}+\frac{2}{3}+\frac{1}{4}\)
\(=\left(\frac{1}{2}+\frac{1}{2}\right)+\left(\frac{3}{4}+\frac{1}{4}\right)+\left(\frac{1}{2}+\frac{2}{3}\right)\)
\(=1+1+\frac{7}{6}\)
\(=2+\frac{7}{6}=\frac{19}{6}.\)