A= 4+2.2+2.2.2+2.2.2.2+.......+{2.2.2.2.2.....} có 20 thừa số 2 

Có số số hạng ở trong khoảng số 2 là:

(20-2)+1=19(số)

Có 20 thừa số 2 suy ra:20.2=40

Tổng là:

(40+2)*19:2=399

A=4+399

A=403

**** nhé Hương Linh xinh xắn

giải jup mik mai mik đi học

a. \(A=2+2^2+2^3+2^4+2^5+...+2^{200}\)

\(2A=2^2+2^3+2^4+2^5+2^6+...+2^{201}\)

\(2A-A=2^{201}-2\)

b. \(Tacó:2^1=2;2^2=4;2^3=8;2^4=..6;2^5=2;2^6=4;...\)

Cứ dựa theo quy luật trên, ta có:

\(2^{4k+1}=..2;2^{4k+2}=...4;2^{4k+3}=...8;2^{4k}=..6\)

\(=>2^{201}=2^{4.50+1}\)

\(=>2^{101}=...2\)

\(=>2^{201}-2=..2-2\)\(=0\)

Vậy A có tân cùng là 0

\(\Rightarrow\frac{1}{2}A=\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{11}}\)

\(\Rightarrow\) \(\frac{1}{2}A=A-\frac{1}{2}=\frac{1}{2^{10}}-\frac{1}{2}\)

Vậy \(A=\left(\frac{1}{2^{10}}-\frac{1}{2}\right):\frac{1}{2}=\frac{2}{2^{10}}-1\)

Do đó \(A+\frac{1}{2^{10}}=\frac{2}{2^{10}}-1+\frac{2}{10}=1\)

Ta có; \(A=1+2^2+2^4+...+2^{100}\)

\(\Rightarrow4A=2^2A=2^2+2^4+...+2^{102}\)

\(\Rightarrow3A=4A-A=\left(2^2+...+2^{102}\right)-\left(1+...+2^{100}\right)\)

\(\Rightarrow3A=2^{102}-1\Rightarrow A=\frac{2^{102}-1}{3}\)

B= ( 2 + 2^2 + 2^3 + 2^4 + 2^5) + 2^5. ( 2 + 2^2 + 2^3 + 2^4 + 2^5)+....+ 2^95 ( 2 + 2^2 + 2^3 + 2^4 + 2^5)

  = 62.(1 + 2^5 + ... + 2^95 ) chia hết cho 62

Suy ra B chia hết cho 31

 CAM ON NHE DUONG

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a = 2 + 2² + 2³ + ... + 2⁶⁰

2a = 2 . 2 + 2² . 2 + 2³ . 2  + ... + 2⁶⁰ . 2

2a =  2² + 2³ + 2⁴ +  ... + 2⁶¹

2a - a = 2⁶¹ - 2

a = 2⁶¹ - 2

Vậy : a = 2⁶¹ - 2