tui ko bít =))))

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

\(S=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{20}}\)

=>  \(2S=1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{19}}\)

=>  \(2S-S=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{19}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{20}}\right)\)

=>  \(S=1-\frac{1}{2^{20}}\)

muộn mất rồi nhưng dù sao cũng cảm ơn bạn

\(B=1+2+2^2+...+2^6.\)

\(=>4B=2^2+2^3+...+2^8\)\(\left(1\right)\)

\(A=2^2+2^3+...+2^8\)\(\left(2\right)\)

Từ (1) và (2) 

=> A = 4B

\(A=2^{100}-2^{99}-...-2^2-2\)

\(2A=2^{101}-2^{100}-...-2^3-2^2\)

\(2A-A=2^{101}-2^{100}-...-2^3-2^2-2^{100}+2^{99}+...2^2+2\)

\(A=2^{101}-\left(2^{100}-2^{100}+2^{99}-2^{99}+...+2^2-2^2+-2\right)\)

\(A=2^{101}+2\)

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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

2¹⁰⁰  -2⁹⁹=2¹

2⁹⁸-2⁹⁷=2¹

=> từ 2¹ -> 2¹⁰⁰ có 50 số 2¹

=>2¹⁰⁰-2⁹⁹-2⁹⁸-...-2¹=2¹.50=2⁵⁰