A=1/2+1/22+1/23+...+1/22020+1/22021 > B=1/3+1/4+1/5+13/60

Ta có: $A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{2021}}+\frac{1}{2^{2022}}$

$\Rightarrow 2A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2020}}+\frac{1}{2^{2021}}$

$\Rightarrow 2A-A=(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2020}}+\frac{1}{2^{}}$

giải ròi đó nhoa

\(A=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2020}}+\dfrac{1}{2^{2021}}\)

\(\Rightarrow\dfrac{1}{2}A=\dfrac{1}{2}.\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2020}}+\dfrac{1}{2^{2021}}\right)\)\(\Rightarrow\dfrac{1}{2}A=\dfrac{1}{2^2}+\dfrac{1}{2^3}+\dfrac{1}{2^4}+...+\dfrac{1}{2^{2021}}+\dfrac{1}{2^{2022}}\)

\(\Rightarrow A-\dfrac{1}{2}A=\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2020}}+\dfrac{1}{2^{2021}}\right)-\left(\dfrac{1}{2^2}+\dfrac{1}{2^3}+\dfrac{1}{2^4}+...+\dfrac{1}{2^{2021}}+\dfrac{1}{2^{2022}}\right)\)\(\Rightarrow\dfrac{1}{2}A=\dfrac{1}{2}-\dfrac{1}{2^{2022}}\)

\(\Rightarrow\dfrac{1}{2}A=\dfrac{2^{2021}-1}{2^{2022}}\)

\(\Rightarrow A=\dfrac{2^{2021}-1}{2^{2023}}.2=\dfrac{2^{2021}-1}{2^{2021}}\)

Vậy \(A=\dfrac{2^{2021}-1}{2^{2021}}\)

\(2S=2+2^2+...+2^{2022}\\ \Leftrightarrow2S-S=S=2^{2022}-1\)

A = 1 + 2 + 2² + ... + 2²⁰²¹
2A = 2 + 4 + 2³ + ... 2²⁰²²
A = 2²⁰²² - 1

\(A=1+2+2^2+...+2^{2020}+2^{2021}\)

\(2A=2+2^2+2^3+...+2^{2021}+2^{2022}\)

\(2A-A=\left(2+2^2+2^3+...+2^{2021}+2^{2022}\right)-\left(1+2+2^2+...+2^{2020}+2^{2021}\right)\)

\(A=2^{2022}-1\)

2A=2*(1+2+2²+...+2²⁰²⁰)=2+2²+...+2²⁰²¹

^2A-A=(1+2+2²+...+2²⁰²¹)-(1+2+2²+...+2²⁰²⁰)

A=2²⁰²¹-1<2021

Giải:

A=1+2+2²+2³+...+2²⁰²⁰

2A=2+2²+2³+2⁴+...+2²⁰²¹

2A-A=(2+2²+2³+2⁴+...+2²⁰²¹)-(1+2+2²+2³+...+2²⁰²⁰)

A=2²⁰²¹-1

⇒A<2²⁰²¹

Chúc bạn học tốt!

\(S=1+2+2^2+2^3+2^4+...+2^{2011}\)

\(\Rightarrow S=\left(1+2+2^2\right)+2^3\left(1+2+2^2\right)+...+2^{2009}\left(1+2+2^2\right)\)

\(\Rightarrow S=7+2^3.7+...+2^{2009}.7\)

\(\Rightarrow S=7\left(1+2^3+...+2^{2009}\right)⋮7\)

\(\Rightarrow dpcm\)

Bài 1

a, cm : A = 16⁵ + 2¹⁵ ⋮ 3

    A = 16⁵ + 2¹⁵

   A = (2⁴)⁵ +  2¹⁵

  A  = 2²⁰ + 2¹⁵

 A  =  2¹⁵.(2⁵ + 1)

 A = 2¹⁵. 33 ⋮ 3 (đpcm)

b,cm : B = 8⁸ + 2²⁰ ⋮ 17

    B = (2³)⁸ + 2²⁰ 

    B =  2¹⁶ + 2²⁰

    B = 2¹⁶.(1 + 2⁴)

    B = 2¹⁶. 17 ⋮ 17 (đpcm)

c, cm: C = 1 - 2 + 2² - 2³ + 2⁴ - 2⁵ + 2⁶ -...-2²⁰²¹ + 2²⁰²² : 6 dư 1

C=1+(-2+2²-2³+2⁴- 2⁵+2⁶)+...+(-2²⁰¹⁷+2²⁰¹⁸-2²⁰¹⁹+2²⁰²⁰-2²⁰²¹+2²⁰²²)

C = 1 + 42 +...+ 2²⁰¹⁶.(-2 + 2² - 2³ + 2⁴ - 2⁵ + 2⁶)

C = 1 + 42+...+ 2²⁰¹⁶.42

C = 1 + 42.(2⁰+...+2²⁰¹⁶)

42 ⋮ 6 ⇒ C = 1 + 42.(2⁰+...+2²⁰¹⁶) : 6 dư 1 đpcm

a, \(\overline{aaa}\) \(⋮\) 37

    \(\overline{aaa}\) = a x 111 = a x 3 x 37 ⋮ 37 (đpcm)

b, (\(\overline{ab}\) + \(\overline{ba}\)) ⋮ 11

  \(\overline{ab}\) + \(\overline{ba}\) = \(\overline{a0}\) + b + \(\overline{b0}\) + a = \(\overline{aa}\) + \(\overline{bb}\) = a x 11 + b x 11 = 11 x (a+b)⋮11

ảnh lỗi kìa làm lại đi bạn ê

Có ai thấy ảnh ko ?

Câu 5 nhé

A = 1/2 + 1/2² + 1/2³ + 1/2⁴+...+ 1/2²⁰²¹ + 1/2²⁰²²

và B = 1/3+1/4+1/5+17/60

Hỏi :

a) Rút gọn A

  b)So sánh A và B