so sánh
a) \(\frac{1}{5^{199}}\)và \(\frac{1}{3^{300}}\)
b) \(\frac{1}{3^{17}}\)và \(\frac{1}{5^{11}}\)
Những câu hỏi liên quan
so sánh
a)\(\frac{1}{5^{199}}\)và \(\frac{1}{3^{300}}\)
b) \(\frac{1}{3^{17}}\)và \(\frac{1}{5^{11}}\)
c) \(\frac{a+1}{a}\)và \(\frac{a+3}{a+2}\)
d) \(\frac{a}{a+6}\)và \(\frac{a+1}{a+7}\)
c) \(\frac{a+1}{a}<\frac{a+1+2}{a+2}=\frac{a+3}{a+2}\) (áp dụng công thức \(\frac{a}{b}<\frac{a+m}{b+m}\))
\(\Rightarrow\frac{a+1}{a}<\frac{a+3}{a+2}\)
d) \(\frac{a}{a+6}<\frac{a+1}{a+6+1}=\frac{a+1}{a+7}\)
\(\Rightarrow\frac{a}{a+6}<\frac{a+1}{a+7}\)
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So sánh phân số saua, frac{1985.1987-1}{1980+1985.1986}và 1b, frac{18}{53}và frac{26}{79}c,frac{5}{8}và frac{14}{17}d, frac{1}{5^{199}}và frac{1}{3^{300}}e, frac{1}{3^{17}}và frac{1}{5^{10}}g, frac{18}{109} và frac{5}{30}
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So sánh phân số sau
a, \(\frac{1985.1987-1}{1980+1985.1986}\)và 1
b, \(\frac{18}{53}\)và \(\frac{26}{79}\)
c,\(\frac{5}{8}\)và \(\frac{14}{17}\)
d, \(\frac{1}{5^{199}}\)và \(\frac{1}{3^{300}}\)
e, \(\frac{1}{3^{17}}\)và \(\frac{1}{5^{10}}\)
g, \(\frac{18}{109}\) và \(\frac{5}{30}\)
Bài 5 : Chững minh rẳng :
a) S frac{3}{10}+frac{3}{11}+frac{3}{12}+frac{3}{13}+frac{3}{14} CMR :1 S 2
b) frac{1}{4^2}+frac{1}{6^2}+frac{1}{8^2}+frac{1}{10^2}+...+frac{1}{left(2nright)^2} frac{1}{4}
c) frac{3}{4}+frac{8}{9}+frac{15}{16}+...+frac{2499}{2500}48
d) frac{1}{5}+frac{1}{13}+frac{1}{14}+frac{1}{15}+frac{1}{61}+frac{1}{62}+frac{1}{63} frac{1}{2}
Bài :So sánh phân số sau:
a)frac{1985.1987-1}{1980+1985.1986}và1
b) A frac{13^{15}+1}{13^{16}+1}và...
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Bài 5 : Chững minh rẳng :
a) S= \(\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}\) CMR :1< S <2
b) \(\frac{1}{4^2}+\frac{1}{6^2}+\frac{1}{8^2}+\frac{1}{10^2}+...+\frac{1}{\left(2n\right)^2}< \frac{1}{4}\)
c) \(\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{2499}{2500}>48\)
d) \(\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}< \frac{1}{2}\)
Bài :So sánh phân số sau:
a)\(\frac{1985.1987-1}{1980+1985.1986}và1\)
b) A= \(\frac{13^{15}+1}{13^{16}+1}\)và B = \(\frac{13^{16}+1}{13^{17}+1}\)
c)\(\frac{18}{53}và\frac{26}{79}\)
d)\(\frac{5}{8}và\frac{14}{17}\)
e)\(\frac{1}{5^{199}}và\frac{1}{3^{300}}\)
g)\(\frac{1}{3^{17}}và\frac{1}{5^{10}}\)
h) \(\frac{18}{109}và\frac{5}{30}\)
\(\frac{1}{5^{199}}\) và \(\frac{1}{3^{300}}\)
Hãy so sánh hai phân số trên
\(3^{300}=\left(3^3\right)^{100}=27^{100}\)
\(5^{199}< 5^{200}\) mà \(5^{200}=25^{100}\)
\(25^{100}< 27^{100}\Rightarrow3^{300}>5^{200}>5^{199}\)
Trong hai phân số cùng tử nếu mẫu nào lớn hớn thì phân số đó bé hơn.
Vậy : \(\frac{1}{5^{199}}>\frac{1}{3^{300}}\)
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So sánh \(\frac{1}{5^{199}}\) và \(\frac{1}{3^{300}}\)
1. Tính nhanh:a.frac{17}{13}timesfrac{7}{15}-frac{5}{12}timesfrac{21}{39}+frac{49}{91}timesfrac{8}{15}b.left(frac{12}{199}+frac{23}{200}-frac{34}{201}right)timesleft(frac{1}{2}-frac{1}{3}-frac{1}{6}right)2. So sánh:a. 3200và2300b. 7150và3775c.frac{201201}{202202}vàfrac{201201201}{202202202}
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1. Tính nhanh:
a.\(\frac{17}{13}\times\frac{7}{15}-\frac{5}{12}\times\frac{21}{39}+\frac{49}{91}\times\frac{8}{15}\)
b.\(\left(\frac{12}{199}+\frac{23}{200}-\frac{34}{201}\right)\times\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)
2. So sánh:
a. 3200và2300
b. 7150và3775
c.\(\frac{201201}{202202}\)và\(\frac{201201201}{202202202}\)
2. a) \(3^{200}=\left(3^2\right)^{100}=9^{100}\)
\(2^{300}=\left(2^3\right)^{100}=8^{100}\)
Vì \(9^{100}>8^{100}\Rightarrow3^{200}>2^{300}\)
b) \(71^{50}=\left(71^2\right)^{25}=5041^{25}\)
\(37^{75}=\left(3^3\right)^{25}=27^{25}\)
Vì \(5041^{25}>27^{25}\Rightarrow71^{50}>37^{75}\)
c) \(\frac{201201}{202202}=\frac{201201:1001}{202202:1001}=\frac{201}{202}\)
\(\frac{201201201}{202202202}=\frac{201201201:1001001}{202202202:1001001}=\frac{201}{202}\)
Vì \(\frac{201}{202}=\frac{201}{202}\Rightarrow\frac{201201}{202202}=\frac{201201201}{202202202}\)
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1.So sánh A và B:
\(A=\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2010}\)và \(B=\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+..........+\frac{1}{17}\)
\(A=\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2010}\)
\(A=\frac{4064340600}{4066362660}+\frac{4064341605}{4066362660}+\frac{4070408792}{4066362660}\)
\(A=3,000000742\)
\(B=\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+....+\frac{1}{17}\)
\(B=1,939552553\)
vì đây là so sánh hai dòng phân số nên ta đổi ra thập phân nhé
do 3,000000742 > 1,939552553 và 3 > 1 Nên A > B nhé
đúng thì k nhé
chúc học giỏi !!!!
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So sánh A và B nếu :
\(A=-\frac{1}{2011}-\frac{3}{11^2}-\frac{5}{11^3}-\frac{7}{11^4}\)va \(B=\frac{1}{2022}-\frac{7}{11^2}-\frac{5}{11^3}-\frac{3}{11^4}\)
So sánh A và B
\(A=-\frac{1}{2011}-\frac{3}{11^2}-\frac{5}{11^3}-\frac{7}{11^4}\)
\(B=-\frac{1}{2011}-\frac{7}{11^2}-\frac{5}{11^3}-\frac{3}{11^4}\)
\(\text{A = }\frac{\text{-1}}{\text{2011}}-\frac{\text{3}}{\text{11}^2}-\frac{\text{5}}{\text{11}^2.\text{11}}-\frac{\text{7}}{\text{11}^2.\text{11}^2}=\text{ }\frac{\text{-1}}{\text{2011}}-\frac{\text{1}}{\text{11}^2}.\left(3-\frac{\text{5}}{\text{11}}-\frac{\text{7}}{\text{11}^2}\right)\)
\(\text{B = }\text{ }\frac{\text{-1}}{\text{2011}}-\frac{7}{\text{11}^2}-\frac{5}{\text{11}^2.\text{11}}-\frac{3}{\text{11}^2.\text{11}^2}=\frac{\text{-1}}{\text{2011}}-\frac{\text{1}}{\text{11}^2}.\left(7-\frac{5}{\text{11}}-\frac{3}{\text{11}^2}\right)\)
\(\text{Vì }3-\frac{\text{5}}{\text{11}}-\frac{\text{7}}{\text{11}^2}< 7-\frac{5}{\text{11}}-\frac{3}{\text{11}^2}\)
\(\Rightarrow\frac{\text{-1}}{\text{2011}}-\frac{\text{1}}{\text{11}^2}.\left(3-\frac{\text{5}}{\text{11}}-\frac{\text{7}}{\text{11}^2}\right)>\frac{\text{-1}}{\text{2011}}-\frac{\text{1}}{\text{11}^2}.\left(7-\frac{5}{\text{11}}-\frac{3}{\text{11}^2}\right)\)
=> A > B
Vậy A > B