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Lời giải:
$1+2+3+....+25$
$=(1+25)+(2+24)+(3+23)+(4+22)+(5+21)+(6+20)+(7+19)+(8+18)+(9+17)+(10+16)+(11+15)+(12+14)+13$
$=\underbrace{26+26+26+...+26}_{12}+13$
$=26\times 12+13=325$
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+34+25+26+27+28+29+30=475
\(a.=\left(\dfrac{4}{5}.\dfrac{5}{6}\right).\dfrac{2}{3}=\dfrac{4}{6}.\dfrac{2}{3}=\dfrac{4}{9}\)
\(b.\dfrac{4}{5}.\dfrac{3}{4}+\dfrac{5}{4}.\dfrac{3}{4}=\dfrac{3}{5}+\dfrac{15}{16}=\dfrac{123}{80}\)
\(c.\left(\dfrac{11}{23}+\dfrac{9}{23}\right)+\left(\dfrac{2}{23}+\dfrac{18}{23}\right)=\dfrac{20}{23}+\dfrac{20}{23}=\dfrac{40}{23}\)
\(d.\left(\dfrac{27}{12}-\dfrac{25}{36}\right)+\left(\dfrac{17}{6}-\dfrac{15}{6}\right)=\dfrac{14}{9}+\dfrac{1}{3}=\dfrac{17}{9}\)
=(25+15)+(36+34)+(27+23)+(28+52)+(19+31)
=40+70+50+80+50
=(50+50)+(80+40)+70
=100+120+70
=220+70
=290
25+36+27+28+19+15+34+23+52+31
=(25+15)+(36+34)+(27+23)+(28+52)+(19+31)
=40+60+50+80+50
=(40+60)+(50+50)+80
=100+100+80
=280