Question

Chứng minh rằng

2 + 2² + 2³ + ... + 2⁸ + 2⁹ \(⋮\) 14

Answer 1

Lời giải:

Ta có:

\(A=2+2^2+2^3+....+2^9\)

\(A=(2+2^2+2^3)+(2^4+2^5+2^6)+(2^7+2^8+2^9)\)

\(A=2(1+2+2^2)+2^4(1+2+2^2)+2^7(1+2+2^2)\)

\(A=2.7+2^4.7+2^7.7\)

\(A=14(1+2^3+2^6)\Rightarrow A\vdots 14\)

Do đó ta có đpcm.

Answer 2

2 + 2² + 2³ + ... + 2⁸ + 2⁹

=(2+2²+2³)+........+(2⁷+2⁸+2⁹)

=2(1+2+2²)+.....+2⁷(1+2+22)

=2.7+......+2⁷.7

=7(2+...+2⁷)

=7.2(1+....+2⁶)

=14(1+....+2⁶)⋮14(đpcm)