Question

a, cho A = 2 + 2^2 + 2^3 + ...... + 2^60 chứng minh A : 3

b, cho B = 3 +3^2 + 3^3 + .....+ 3^20 chứng minh B là bội của 12

Answer 1

a, \(A=2+2^2+2^3+....+2^{60}\)

\(=\left(2+2^2\right)+\left(2^3+2^4\right)+....+\left(2^{59}+2^{60}\right)\)

\(=2.\left(1+2\right)+2^3.\left(1+2\right)+....+2^{59}.\left(1+2\right)\)

\(=2.3+2^3.3+....+2^{59}.3\)

\(=3.\left(2+2^3+...+2^{59}\right)⋮3\)(đpcm)