Câu hỏi của Tường Vi Trắng

Question

Chứng minh rằng:

S=2²⁰⁰⁰+2²⁰⁰¹+...+2²⁰⁰⁵chia hết cho 7

Nguyễn Ngọc Quý · Accepted Answer

$S=2^{2000}+2^{2001}+2^{2002}+2^{2003}+2^{2004}+2^{2005}$

$S=\left(2^{2000}+2^{2001}+2^{2002}\right)+\left(2^{2003}+2^{2004}+2^{2005}\right)$

$S=\left(2^{2000}.1+2^{2000}.2+2^{2000}.4\right)+\left(2^{2003}.1+2^{2003}.2+3^{2003}.4\right)$

$S=2^{2000}.\left(1+2+4\right)+2^{2003}.\left(1+2+4\right)$$S=2^{2000}.7+2^{2003}.7=7.\left(2^{2000}+2^{2003}\right)$

Vậy S chia hết cho 7

Câu trả lời:

$S=2^{2000}+2^{2001}+2^{2002}+2^{2003}+2^{2004}+2^{2005}$

$S=\left(2^{2000}+2^{2001}+2^{2002}\right)+\left(2^{2003}+2^{2004}+2^{2005}\right)$

$S=\left(2^{2000}.1+2^{2000}.2+2^{2000}.4\right)+\left(2^{2003}.1+2^{2003}.2+3^{2003}.4\right)$

$S=2^{2000}.\left(1+2+4\right)+2^{2003}.\left(1+2+4\right)$$S=2^{2000}.7+2^{2003}.7=7.\left(2^{2000}+2^{2003}\right)$

Vậy S chia hết cho 7

Nguyễn Đức Mạnh · Answer

Ta có

S= 2^2000+2^2001+2^2002+2^2003+2^2004+2^2005

S=(2^2000+2^2001+2^2002)+(2^2003+2^2004+2^2005)

S=2^2000(1+2+2^2)+2^2003(1+2+2^2)

S=2^2000(1+2+4)+2^2003(1+2+4)

S=2^2000*7+2^2003*7

S=7(2^2000+2^2003)

Ta thấy 7(2^2000+2^2003) chia hết cho 7 nên Schia hết cho 7

Vậy S chia hết cho 7 (đpcm) tick nha bạn