A = 2016 x 2016 x ... x 2016
= 2016²⁰¹⁵
= \(\overline{...6}\)
B = 2017 x 2017 x ... x 2017
= 2017²⁰¹⁶
= 2017^504.4
= (2017⁴)⁵⁰⁴
= (\(\overline{...1}\))⁵⁰⁴
= \(\overline{...1}\)
=> A + B = \(\overline{...6}+\overline{...1}=\overline{...7}\) không chia hết cho 5
@Cỏ Ba Lá

\(2016^{2015}\)

Giúp mk với mọi người

câu 1. tìm x nguyên để \(\frac{-35}{6}\)<x<\(\frac{-18}{5}\)

<=> -4,375<x<-3,6

mà x\(\in\)Z nên x={-4}

câu 2. A=\(\frac{2015}{2016}\)+\(\frac{2016}{2017}\)

B=\(\frac{2015+2016}{2016+2017}\)=\(\frac{2015}{2016+2017}\)+\(\frac{2016}{2016+2017}\)

Vì \(\frac{2015}{2016+2017}\)<\(\frac{2015}{2016}\); \(\frac{2016}{2016+2017}\)<\(\frac{2016}{2017}\)

Vậy B<A

cau3:

\(\frac{1}{3}\)+\(\frac{1}{6}\)+\(\frac{1}{10}\)+.....+\(\frac{2}{x\left(x+1\right)}\)=\(\frac{2007}{2009}\)

2.(\(\frac{1}{6}\)+\(\frac{1}{12}\)+\(\frac{1}{20}\)+.....+\(\frac{1}{x\left(x+1\right)}\))=\(\frac{2007}{2009}\)

2.(\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+\(\frac{1}{4.5}\)+.....+\(\frac{1}{x\left(x+1\right)}\))=\(\frac{2007}{2009}\)

2.(\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+\(\frac{1}{4}\)-\(\frac{1}{5}\)+.....+\(\frac{1}{x}\)-\(\frac{1}{x+1}\))=\(\frac{2007}{2009}\)

2.(\(\frac{1}{2}\)-\(\frac{1}{x+1}\))=\(\frac{2007}{2009}\)

\(\frac{1}{2}\)-\(\frac{1}{x+1}\)=\(\frac{2007}{4018}\)

\(\frac{1}{x+1}\)=\(\frac{1}{2}\)-\(\frac{2007}{4018}\)

\(\frac{1}{x+1}\)=\(\frac{1}{2009}\)

x+1=2009

x=2009-1

x=2008

. là nhân đó nha

Ta có : 

\(A=2016.2016.....2016=2016^{2015}\) 

\(B=2017.2017.....2017\)

\(B=2017^{2016}\)

\(B=\left(2016+1\right)^{2016}\)

\(B=2016^{2016}+4032+1\)

\(\Rightarrow\)\(A+B=2016^{2015}+2016^{2016}+4032+1\)

\(\Rightarrow\)\(A+B=2016^{2015}.2017+4033\)

Lại có : 

\(2016^{2015}\) luôn có chữ số tận cùng là \(6\)

\(\Rightarrow\)\(2016^{2015}.2017\) có chữ số tận cùng là \(2\)

\(\Rightarrow\)\(2016^{2015}.2017+4033\) có chữ số tận cùng là \(5\)

Do đó : 

\(A+B\) chia hết cho \(5\)

Vậy \(A+B\) chia hết cho \(5\)

Chúc bạn học tốt ~ 

ở chỗ 4032 sao ra bn?