Question

Chứng tỏ rằng:  A=2+2²+2³+2⁴+....+2⁹⁰ chia hết cho 21

Answer 1

\(A=2+2^2+2^3+............+2^{90}\)

\(A=\left(2+2^2+2^3+2^4+2^5+2^6\right)+.............+\left(2^{85}+2^{86}+2^{87}+2^{88}+2^{89}+2^{90}\right)\)

\(A=2.3.21+2^7.3.21+...........+2^{85}.3.21\)

\(A=21.3.\left(2+2^7+.......+2^{85}\right)\)

=> A chia hết cho 21