a, Có : (1/60)^200 = [(1/2)^4]^200 = (1/2)^800

Vì 0 < 1/2 < 1 nên (1/2)^800 > (1/2)^1000

=> (1/16)^200 > (1/2)^1000

Tk mk nha

a) \(\left(\frac{1}{16}\right)^{200}=\left(\frac{1}{2}\right)^{800}< \left(\frac{1}{2}\right)^{1000}\)

a) \(\left(\frac{1}{16}\right)^{200}=\frac{1}{16^{200}}\)

\(\left(\frac{1}{2}\right)^{1000}=\frac{1}{2^{1000}}\)

có : \(16^{200}=\left(2^4\right)^{200}=2^{800}\)

ta thấy \(2^{800}< 2^{1000}\)

\(\Rightarrow16^{200}< 2^{1000}\)

\(\Rightarrow\frac{1}{16^{200}}>\frac{1}{2^{1000}}\)

\(\Rightarrow\left(\frac{1}{16}\right)^{200}>\left(\frac{1}{2}\right)^{100}\)

\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{1000}}\)

\(2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{999}}\)

\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{999}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{1000}}\right)\)

\(A=1-\frac{1}{2^{1000}}< 1=B\)

`Answer:`

Đặt \(C=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{999.1000}\)

Ta thấy:

\(\frac{1}{1.2}>\frac{1}{2^2}\)

\(\frac{1}{2.3}>\frac{1}{2^3}\)

\(\frac{1}{3.4}>\frac{1}{2^4}\)

...

\(\frac{1}{999.1000}>\frac{1}{2^{1000}}\)

\(\Rightarrow\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{1000}}< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{999.1000}\)

\(\Rightarrow A< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{4}+\frac{1}{5}-\frac{1}{5}+...+\frac{1}{999}-\frac{1}{1000}\)

\(\Rightarrow A< 1-\frac{1}{1000}\)

Mà \(\frac{1}{1000}>0\)

\(\Rightarrow1-\frac{1}{1000}< 1\)

\(\Rightarrow C< B\)

\(\Rightarrow A< C< B\)

\(\Rightarrow A< B\)

so sánh : \(\dfrac{1}{35}\) và \(\dfrac{1000}{-35}\)

có : \(\dfrac{1000}{-35}\) = \(\dfrac{-1000}{35}\)

\(\Rightarrow\) \(1\) \(>\) (\(-1000\) )

\(\Rightarrow\) \(\dfrac{1}{35}\) \(< \) \(\dfrac{-1000}{35}\)

vậy : \(\dfrac{1}{35}\) < \(\dfrac{1000}{-35}\) hay \(\dfrac{1000}{-35}\) > \(\dfrac{1}{35}\)

1/35>1000/-35

a: \(\left(-\dfrac{1}{16}\right)^{100}=\left(\dfrac{1}{16}\right)^{100}=\left(-\dfrac{1}{2}\right)^{400}\)

\(\left(-\dfrac{1}{2}\right)^{500}=\left(-\dfrac{1}{2}\right)^{500}\)

mà \(400< 500\)

nên \(\left(-\dfrac{1}{16}\right)^{100}< \left(-\dfrac{1}{2}\right)^{500}\)

A=1+2+3+...+1000

A=(1000+1).1000/2

A=500500

B=1.2.3...11

B=11!

B=39916800

39916800>500500

B>A

a) 16⁴ = (2⁴)⁴ = 2¹⁶

8⁵ = (2³)⁵ = 2¹⁵

Vì 2¹⁶>2¹⁵ nên 16⁴>8⁵

b) 27⁷=(3³)⁷=3²¹

9¹⁰=(3²)¹⁰=3²⁰

Vì 3²¹>3²⁰ nên 27⁷>9¹⁰

c) 2³⁰⁰=(2³)¹⁰⁰=8¹⁰⁰

3²⁰⁰=(3²)¹⁰⁰=9¹⁰⁰

Vì 8¹⁰⁰ < 9¹⁰⁰ nên 2³⁰⁰ < 3²⁰⁰

a,16⁴>8⁵

b,27⁷>9¹⁰

c,2³⁰⁰ <3²⁰⁰

nhé bạn

A

6^4=(2^4}^1=+2^64

8^5=(2^2}^5=2^1O

64 lớn hơn 1O

nên 2^64 lớn hơn 2^1O

vậy 6^4 lớn hơn 8^5

b

27^7=(3^3}^7=3^21

9^1O=(3^2}^1O=3^2O

21 lớn hơn 2O

nên 3^21 lớn hơn 3^2O

vậy 27^7 lớn hơn 9^1O

c

2^3OO=2^3.1OO=6^1OO

3^2OO=3^2.1OO=6^1OO

1OO=1OO

nên 6^1OO=6^1OO

vậy 2^3OO=3^2OO