Question

B=​​​​\(^{2+2^2+2^3+...+2^{59}+2^{60}}\)

a, chung to rang B chia het cho 3,5,7

b,tim chu so tan cung cua B

Answer 1

B = 2+2²+2³+....+2⁵⁹+2⁶⁰

B = (2+2²+2³+2⁴) +....+ (2⁵⁷+2⁵⁸+5⁵⁹+5⁶⁰)

B = 2(1+2+2²+2³)+...+ 2⁵⁷(1+2+2²+2³)

B = 2x15 +....+ 2⁵⁷x15

B = 15( 2+....+2⁵⁷) =>chia hết cho 5 vì 15 chia hết cho 5

Answer 2

a) B=2+2² + 2³ + ...+ 2^{59 +} 2⁶⁰

B= (2+2²) + (2³+2⁴) + .... + ( 2⁵⁹+ 2⁶⁰)

B= 2(1+2) + 2³(1+2) + ... +2⁵⁹(1+2)

B= 2x3 + 2³x3 + ... + 2⁵⁹x3

B= 3(2+2³+......+2⁵⁹) => chia hết cho 3

Answer 3

B = 2+2²+2³+...+2⁵⁹+2⁶⁰

B = (2+2²+2³)+....+( 2⁵⁸+2⁵⁹+2⁶⁰)

B = 2(1+2+2²) +...+ 2⁵⁸(1+2+2²)

B = 2x7 +...+ 2⁵⁸x7 

B = 7(2+...+2⁵⁸) => chia hết cho 7