cho C=7^200+1/7^202+1
D=205+1/7^207+1 so sanh C va D
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BH
22 tháng 3 2019
Ta có \(7^{200}< 7^{205}\Rightarrow7^{200}+1< 7^{205}+1\Rightarrow\frac{7^{200}+1}{7^{202}+1}< \frac{7^{205}+1}{7^{202}+1}\)
22 tháng 3 2019
vi 7200 + 1 < 7205 + 1 => \(\frac{7^{200}+1}{7^{202}+1}< \frac{7^{205}+1}{7^{202}+1}\)
=> \(A< B\)
T
1
10 tháng 9 2015
^ là mũ nhé
2^300 = (2^3)^100=8^100 ; 3^200 = (3^2)^100 = 9^100
Mà 9 > 8 => 8^100 < 9^100
Vậy 2^300 < 3^200
99^20 = (99^2)^10 = 9801^10 và 9999^10
Mà 9999 > 9801 => 9801^10 < 9999^10
Vậy 99^20 < 9999^10
3^500 = (3^5)^100 = 243^100
7^300 = (7^3)^100 = 343^100
Mà 343 > 243 => 343^100 > 243^100
Vậy 3^500 < 7^300
202^303 = (202^3)^101 = 8242408^101 ; 303^202 = (303^2)^101 = 91204
Vậy 202^303 > 303^202
NT
2
KL
18 tháng 8 2017
a, A = 3500 = (35)100 = 243100
B = 7300 = (73)100 = 343100
Mà 243100 < 343100
=> A < B
@nguyễn thi trà giang
16 tháng 9 2017
a) \(A=3^{500}=\left(3^5\right)^{100}=243^{100}\)
\(B=7^{300}=\left(7^3\right)^{100}=343^{100}\)
Vì \(243^{100}< 343^{100}\Rightarrow3^{500}< 7^{300}\)
\(\Rightarrow A< B\)
b) \(A=303^{202}=\left(303^2\right)^{101}=91809^{101}\)
\(B=202^{303}=\left(202^3\right)^{101}=8242408^{101}\)
Vì \(91809^{101}< 8242408^{101}\Rightarrow303^{202}< 202^{303}\)
\(\Rightarrow A< B\)
c) \(A=3^{21}=3\cdot3^{20}=3\cdot\left(3^2\right)^{10}=3\cdot9^{10}\)
\(B=2^{31}=2\cdot2^{30}=2\cdot\left(2^3\right)^{10}=2\cdot8^{10}\)
Ta có: \(3>2;9^{10}>8^{10}\Rightarrow3\cdot9^{10}>2\cdot8^{10}\Rightarrow3^{21}>2^{31}\)
\(\Rightarrow A< B\)
NC
2
CT
Cô Tuyết Ngọc
Manager
VIP
29 tháng 3 2023
em nên gõ công thức trực quan để được hỗ trợ tốt nhất nhé
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
29 tháng 3 2023
D = \(\dfrac{1}{7^2}\) - \(\dfrac{2}{7^3}\) + \(\dfrac{3}{7^4}\) - \(\dfrac{4}{7^5}\) +........+ \(\dfrac{201}{7^{202}}\) - \(\dfrac{202}{7^{203}}\)
7 \(\times\) D = \(\dfrac{1}{7}\) - \(\dfrac{2}{7^2}\) + \(\dfrac{3}{7^3}\) - \(\dfrac{4}{7^4}\) + \(\dfrac{5}{7^5}\) -.......- \(\dfrac{202}{7^{202}}\)
7D +D = \(\dfrac{1}{7}\) - \(\dfrac{1}{7^2}\) + \(\dfrac{1}{7^3}\) - \(\dfrac{1}{7^4}\) + \(\dfrac{1}{7^5}\) -.........-\(\dfrac{1}{7^{202}}\) - \(\dfrac{202}{7^{203}}\)
D = ( \(\dfrac{1}{7}\) - \(\dfrac{1}{7^2}\) + \(\dfrac{1}{7^3}\) - \(\dfrac{1}{7^4}\) + \(\dfrac{1}{7^5}\) -.........-\(\dfrac{1}{7^{202}}\) - \(\dfrac{202}{7^{203}}\)) : 8
Đặt B = \(\dfrac{1}{7}\) - \(\dfrac{1}{7^2}\) + \(\dfrac{1}{7^3}\) - \(\dfrac{1}{7^4}\) + \(\dfrac{1}{7^5}\) -........+\(\dfrac{1}{7^{201}}\).-\(\dfrac{1}{7^{202}}\)
7 \(\times\) B = 1 - \(\dfrac{1}{7}\)+\(\dfrac{1}{7^2}\) - \(\dfrac{1}{7^3}\) + \(\dfrac{1}{7^4}\) - \(\dfrac{1}{7^5}\) +.........- \(\dfrac{1}{7^{201}}\)
7B + B = 1 - \(\dfrac{1}{7^{202}}\)
B = ( 1 - \(\dfrac{1}{7^{202}}\)) : 8
D = [ ( 1 - \(\dfrac{1}{7^{202}}\)): 8 - \(\dfrac{202}{7^{203}}\)] : 8
D = \(\dfrac{1}{64}\) - \(\dfrac{1}{64.7^{202}}\) - \(\dfrac{202}{7^{203}.8}\) < \(\dfrac{1}{64}\)
Q
23 tháng 6 2017
a) Ta có:
+) \(\dfrac{1}{2}=\dfrac{3}{6}\)
+) \(\dfrac{1}{3}=\dfrac{2}{6}\)
+) \(\dfrac{2}{3}=\dfrac{4}{6}\)
=> \(\dfrac{2}{6}< \dfrac{3}{6}< \dfrac{4}{6}\)
hay \(\dfrac{1}{3}< \dfrac{1}{2}< \dfrac{2}{3}\)
b) Ta có:
+) \(\dfrac{4}{9}=\dfrac{56}{126}\)
+) \(-\dfrac{1}{2}=-\dfrac{63}{126}\)
+) \(\dfrac{3}{7}=\dfrac{54}{126}\)
=> \(-\dfrac{63}{126}< \dfrac{54}{126}< \dfrac{56}{126}\)
hay \(-\dfrac{1}{2}< \dfrac{3}{7}< \dfrac{4}{9}\)
c) Ta có:
+) \(\dfrac{27}{82}=\dfrac{2025}{6150}\)
+) \(\dfrac{26}{75}=\dfrac{2132}{6150}\)
=> \(\dfrac{2025}{6150}< \dfrac{2132}{6150}\)
hay \(\dfrac{27}{82}< \dfrac{26}{75}\)
d) Ta có:
+) \(-\dfrac{49}{78}=-\dfrac{4655}{7410}\)
+) \(-\dfrac{64}{95}=-\dfrac{4992}{7410}\)
=> \(-\dfrac{4665}{7410}>-\dfrac{4992}{7410}\)
hay \(-\dfrac{49}{78}>-\dfrac{64}{95}\)
NN
2
DP
12 tháng 4 2017
\(\frac{201}{202}+\frac{202}{205}\)Và \(201+\frac{202}{202}+205\)
\(=\frac{201}{202}=\frac{201}{202}+\frac{1}{202}=\frac{202}{202}\)
\(\frac{202}{205}=\frac{202}{205}+\frac{3}{205}=\frac{205}{205}\)
\(201+1+205\)
Vậy \(1+1=2\)và \(407\)
=> \(\frac{201}{202}+\frac{202}{205}< 201+\frac{202}{202}+205\)
D
12 tháng 4 2017
Ta có: \(\frac{201+202}{202+205}=\frac{201}{202+205}+\frac{202}{202+205}\)
Ta có: 202<202+205 => \(\frac{201}{202}>\frac{201}{202+205}\)(1)
205<202+205 => \(\frac{202}{205}>\frac{202}{202+205}\)(2)
Từ (1) và (2) => \(\frac{201}{202}+\frac{202}{205}>\frac{201+202}{202+205}\)
