Giúp mk với ạ.Mình cần gấ ạ.Ai nhanh mk K ạ.
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Ta có: 1/4 < (1+1)/(4+1) = 2/5
3/6 < (3+1)/(6+1) = 4/7
.......................
995/998 < (995+1)/(998+1) = 996/999
997/1000 <(997+1)/(1000+1) =998/1001
( mk sửa đề 1 chút nha )
\(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)
= \(\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)
= \(\frac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)
= \(\frac{2^{29}.3^{18}.\left(5.2-3^2\right)}{2^{28}.3^{18}.\left(5.3-7.2\right)}\)
= \(\frac{2.1}{1}\)
= 2
Hok tốt
( nhớ ủng hộ mk nha )
Bài làm:
Ta có: \(\frac{7.6^{10}.2^{20}.3^6-2^{19}.6^{15}}{9.6^{19}.2^9-4.3^{17}.2^{26}}\)
\(=\frac{7.2^{10}.3^{10}.2^{20}.3^6-2^{19}.2^{15}.3^{15}}{3^2.2^{19}.3^{19}.2^9-2^2.3^{17}.2^{26}}\)
\(=\frac{2^{30}.3^{16}.7-2^{34}.3^{15}}{2^{28}.3^{21}-2^{28}.3^{17}}\)
\(=\frac{2^{30}.3^{15}\left(3.7-2^4\right)}{2^{28}.3^{17}\left(3^4-1\right)}\)
\(=\frac{2^2\left(21-16\right)}{3^2\left(81-1\right)}\)
\(=\frac{2^2.5}{3^2.80}\)
\(=\frac{1}{36}\)
1/4=1-3/4
2/5=1-3/5
mà 3/4>3/5
nên 1/4<2/5
3/6=1-3/6
4/7=1-3/7
mà 3/6>3/7
nên 3/6<4/7
...
97/100<98/101
=>P=1/4*3/6*5/8*...*97/100<2/5*4/7*...*98/101=Q