Question

ch P= 1+3+3^2+3^3+3^4+3^5+3^6+3^7

chứng minh p chia hết cho 4

 

Answer 1

\(P=1+3+3^2+...+3^7\)

\(=\left(1+3\right)+...+\left(3^6+3^7\right)\)

\(=1\left(1+3\right)+...+3^6\left(1+3\right)\)

\(=1\cdot4+...+3^6\cdot4\)

\(=4\cdot\left(1+...+3^6\right)⋮4\)

Đpcm

Answer 2

p=1+3+3²+3³+3⁴+3⁵+3⁶+3⁷

p=(1+3)+(3²+3³)+(3⁴+3⁵)+(3⁶+3⁷)

p=4.1+(3².1+3².3)+(3⁴.1+3⁴.3)+(3⁶.1+3⁶.3)

p=4.1+3²(1+3)+3⁴(1+3)+3⁶(1+3)

p=4.1+3².4+3⁴.4+3⁶.4

p=4.(1+3²+3⁴+3⁶)

vay P chia het cho 4