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a = (7^2.2^3+6^2.2^3+2.5.2^4-40) : 8
= (7^2.8+6^2.8+2^2.5.8-5.8) : 8
= 7^2+6^2+2^2.5-5 = 49+36+20-5 = 100
k mk nha
do 10^n chia cho 9 dư 1 với mọi n=>2.10^n chia cho 9 dư 2
mà 25 chia cho 9 dư 7 =>B CHIA HẾT CHO 9
cấm copy nha
\(A=\frac{15}{19}\left(\frac{17}{23}+\frac{19}{23}-\frac{13}{23}\right)=\frac{15}{19}\left(\frac{17+19-13}{23}\right)=\frac{15}{19}\cdot\frac{23}{23}=\frac{15}{19}.1=\frac{15}{19}\)
Ta có : \(A=\frac{19^{30}+15}{19^{31}+15}\)
\(\Rightarrow19A=\frac{19^{31}+285}{19^{31}+15}=\frac{19^{31}+15+270}{19^{31}+15}=1+\frac{270}{19^{31}+15}\)
Lại có \(B=\frac{19^{31}+15}{19^{32}+15}\)
\(\Rightarrow19B=\frac{19^{32}+285}{19^{32}+15}=\frac{19^{32}+15+270}{19^{32}+15}=1+\frac{270}{19^{32}+15}\)
Vì \(\frac{270}{19^{32}+15}< \frac{270}{19^{31}+15}\Rightarrow1+\frac{270}{19^{32}+5}< 1+\frac{270}{19^{31}+15}\Rightarrow19B< 19A\Rightarrow B< A\)
\(\dfrac{7}{-25}+\dfrac{18}{25}+\dfrac{4}{23}+\dfrac{5}{7}+\dfrac{19}{23}\)
=\(\left(\dfrac{-7}{25}+\dfrac{18}{25}\right)+\left(\dfrac{4}{23}+\dfrac{19}{23}\right)+\dfrac{5}{7}\)
= \(\dfrac{11}{25} +1+\dfrac{5}{7}\)
= \(1\dfrac{11}{25}+\dfrac{5}{7}\)
= \(2\dfrac{27}{175}\)
b) \(-2+\dfrac{15}{19}+\dfrac{-15}{17}+\dfrac{15}{23}+\dfrac{4}{19}\)
=\(-2+\left(\dfrac{ }{ }\right)\)
M = \(15.\left(\frac{1}{15.16}+\frac{1}{16.17}+...+\frac{1}{19.20}\right)\)
= \(15.\left(\frac{1}{15}-\frac{1}{16}+\frac{1}{16}-\frac{1}{17}+...+\frac{1}{19}-\frac{1}{20}\right)\)
= \(15.\left(\frac{1}{15}-\frac{1}{20}\right)\)
= \(15.\frac{1}{60}\)= \(\frac{1}{4}\)\(< \frac{1}{3}\)
(=) \(M< \frac{1}{3}\)\(\left(đpcm\right)\)
Ta có: \(M=\frac{15}{15.16}+\frac{15}{16.17}+\frac{15}{17.18}+\frac{15}{18.19}+\frac{15}{19.20}\)
\(\Rightarrow M=15.\left(\frac{1}{15.16}+\frac{1}{16.17}+\frac{1}{17.18}+\frac{1}{18.19}+\frac{1}{19.20}\right)\)
\(\Rightarrow M=15.\left(\frac{1}{15}-\frac{1}{16}+\frac{1}{16}-\frac{1}{17}+\frac{1}{17}-\frac{1}{18}+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)
\(\Rightarrow M=15.\left(\frac{1}{15}-\frac{1}{20}\right)\)
\(\Rightarrow M=15.\frac{1}{60}=\frac{1}{4}\)
Ta thấy: \(\frac{1}{4}< \frac{1}{3}\Rightarrow M< \frac{1}{3}\)
Vậy \(M< \frac{1}{3}\)
Chúc bạn học tốt!
5700 nha
=5700( *=x)