28032015:a6b8ba
2803a+aaa-141=13^4
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a)\(\frac{-1}{3}.\frac{141}{17}-13.\frac{-1}{17}\)
\(=\frac{141}{3}.\frac{-1}{17}-13.\frac{-1}{17}\)
\(=47.\frac{-1}{17}-13.\frac{-1}{3}\)
\(=\frac{-1}{17}.\left(47-13\right)\)
\(=\frac{-1}{17}.33=....\)(tự tính)
\(a,\)\(\frac{-1}{3}.\frac{141}{17}-13.\frac{-1}{7}\)
\(=\frac{-1.141}{3.17}+13.\frac{1}{17}\)
\(=\frac{-141}{17}.\frac{1}{7}+13.\frac{1}{7}\)
\(=\frac{1}{7}\left(-47+13\right)\)
\(=\frac{-34}{7}\)
\(b,\)\(\frac{-9}{16}.\frac{13}{3}-\left(-\frac{3}{4}\right)^2.\frac{19}{3}\)
\(=\left(\frac{3}{4}\right)^2.\frac{-13}{3}-\left(-\frac{9}{16}\right).\frac{19}{3}\)
\(=\frac{9}{16}.\frac{-13}{3}+\frac{9}{16}.\frac{19}{3}\)
\(=\frac{9}{16}\left(\frac{-13}{3}+\frac{19}{3}\right)=\frac{9}{16}.2=\frac{9}{8}\)
C=1-2/15+1-2/35+1-2/63+...+1-2/195
\(C=6-\left(\dfrac{2}{3x5}+\dfrac{2}{5x7}+\dfrac{2}{7x9}+...+\dfrac{2}{13x15}\right)=\)
\(=6-\left(\dfrac{5-3}{3x5}+\dfrac{7-5}{5x7}+\dfrac{9-7}{7x9}+...+\dfrac{15-13}{13x15}\right)=\)
\(=6-\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+...+\dfrac{1}{13}-\dfrac{1}{15}\right)=\)
\(=6-\left(\dfrac{1}{5}-\dfrac{1}{15}\right)=\dfrac{88}{15}\)
\(A=1-\frac{2}{3}+1-\frac{2}{15}+1-\frac{2}{35}+1-\frac{2}{63}+1-\frac{2}{99}+1-\frac{2}{143}\)
\(=1+1+1+1+1+1-\frac{2}{3}-\frac{2}{15}-\frac{2}{35}-\frac{2}{63}-\frac{2}{99}-\frac{2}{143}\)
\(=6-\left(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}\right)\)
\(=6-\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\right)\)
\(=6-\left(1-\frac{1}{13}\right)\)
\(=6-1+\frac{1}{13}\)
\(=5+\frac{1}{13}\)
\(=\frac{65}{13}+\frac{1}{13}\)
\(=\frac{66}{13}\)
aaa = a.100+a.10+a.1
= a.(100+10+1)
= a.111
Vì 111chia hết cho 37 nên suy ra số có dạng aaa hay aaaa chia hết cho 37