\(A=\frac{5^5}{5+5^2+5^3+5^4}=\frac{5^4}{1+5+5^2+5^3}=\frac{625}{156}>\frac{468}{156}=3\left(1\right)\)
\(B=\frac{3^5}{3+3^2+3^3+3^4}=\frac{3^4}{1+3+3^2+3^3}=\frac{81}{40}< \frac{120}{40}=3\left(2\right)\)
Từ (1) và (2)=> A>B
Vậy A>B
Các câu hỏi tương tự
Tìm x biết:
a.
\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}.\frac{5}{12}...\frac{30}{62}.\frac{31}{64}=2^x\)
b.
\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^x\)
A)\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}.\frac{5}{12}....\frac{30}{62}.\frac{31}{64}=4^x\)
B)\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=8^x\)
Chứng minh rằng:a. frac{1}{3^2}+frac{2}{3^3}+frac{3}{3^4}+frac{4}{3^5}+...+frac{99}{3^{100}}+frac{100}{3^{101}} frac{1}{4}b.frac{1}{2}-frac{1}{4}+frac{1}{8}-frac{1}{16}+frac{1}{32}-frac{1}{64} frac{1}{3}c.frac{1}{3}-frac{2}{3^2}+frac{3}{3^3}-frac{4}{3^4}+...+frac{99}{3^{99}}-frac{100}{3^{100}} frac{1}{16}d. frac{1}{5^2}-frac{2}{5^3}+frac{3}{5^4}-frac{4}{5^5}+...+frac{99}{5^{100}}-frac{100}{5^{101}} frac{1}{36}
Đọc tiếp
Chứng minh rằng:
a. \(\frac{1}{3^2}+\frac{2}{3^3}+\frac{3}{3^4}+\frac{4}{3^5}+...+\frac{99}{3^{100}}+\frac{100}{3^{101}}< \frac{1}{4}\)
b.\(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}< \frac{1}{3}\)
c.\(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...+\frac{99}{3^{99}}-\frac{100}{3^{100}}< \frac{1}{16}\)
d. \(\frac{1}{5^2}-\frac{2}{5^3}+\frac{3}{5^4}-\frac{4}{5^5}+...+\frac{99}{5^{100}}-\frac{100}{5^{101}}< \frac{1}{36}\)
so sanh
a)\(A=\frac{5}{4}+\frac{5}{4^2}+\frac{5}{4^3}+.....+\frac{5}{4^{99}}vaB=\frac{5}{3}\)
b)\(B=\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+.....+\frac{3^{98}+1}{3^{98}}vaA=100\)
A frac{frac{3}{4}-frac{3}{11}+frac{3}{13}}{frac{5}{4}-frac{5}{11}+frac{5}{13}}+frac{frac{1}{2}-frac{1}{3}+frac{1}{4}}{frac{5}{4}-frac{5}{6}+frac{5}{8}}B frac{2^{12}.3^5-4^6.9^2}{left(2^2.3right)^6+8^4.3^5}-frac{5^{10}.7^3-25^5.49}{left(125.7right)^3+5^9.14^3}C frac{left(a^{2016}+b^{2016}right)^{2017}}{left(c^{2016}+d^{2016}right)^{2017}} frac{left(a^{2017}-b^{2017}right)^{2016}}{left(c^{2017}-d^{2017}right)^{2016}}
Đọc tiếp
A = \(\frac{\frac{3}{4}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{4}-\frac{5}{11}+\frac{5}{13}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}-\frac{5}{6}+\frac{5}{8}}\)
B = \(\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\frac{5^{10}.7^3-25^5.49}{\left(125.7\right)^3+5^9.14^3}\)
C = \(\frac{\left(a^{2016}+b^{2016}\right)^{2017}}{\left(c^{2016}+d^{2016}\right)^{2017}}\)= \(\frac{\left(a^{2017}-b^{2017}\right)^{2016}}{\left(c^{2017}-d^{2017}\right)^{2016}}\)
BT1: Tinh1.Aleft(4-frac{1}{2}+frac{2}{3}right)+left(5+frac{4}{3}-frac{6}{5}right)-left(6-frac{7}{4}+frac{4}{5}right)2.Bfrac{left(-1right)^6.3^5.4^3}{9^2.2^5}3.frac{4}{5}.frac{11}{3}-frac{4}{5}.frac{8}{3}+frac{1}{5}4.sqrt{289-sqrt{169+sqrt{256-sqrt{196}}}}5.frac{3^{15}.2^{18}.5^4}{6^{14}.10^5}
Đọc tiếp
BT1: Tinh
\(1.A=\left(4-\frac{1}{2}+\frac{2}{3}\right)+\left(5+\frac{4}{3}-\frac{6}{5}\right)-\left(6-\frac{7}{4}+\frac{4}{5}\right)\)
\(2.B=\frac{\left(-1\right)^6.3^5.4^3}{9^2.2^5}\)
\(3.\frac{4}{5}.\frac{11}{3}-\frac{4}{5}.\frac{8}{3}+\frac{1}{5}\)
\(4.\sqrt{289-\sqrt{169+\sqrt{256-\sqrt{196}}}}\)
\(5.\frac{3^{15}.2^{18}.5^4}{6^{14}.10^5}\)
A = \(\frac{\frac{-11}{2}+\frac{\frac{-5}{3}}{1-\frac{4}{3}}}{\frac{3}{5}-\frac{\frac{-2}{5}}{\frac{4}{5}-\frac{2}{3}}}\)
7 tháng 1 2020 lúc 20:48
tìm x biết
a, \(\frac{1}{2}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot\frac{4}{10}\cdot...\cdot\frac{30}{62}\cdot\frac{31}{64}=4^x\)
b, \(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}\cdot\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=8^x\)
c,\(\left|4x+3\right|-\left|x-1\right|=7\)
mong các bạn giúp !!!
So sánh : \(A=\frac{5^5}{5+5^2+5^3+5^4}\)và \(B=\frac{3^5}{3+3^2+3^3+3^4}\)