Ta có : 

\(A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{2016}\right)\)

\(A=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{2015}{2016}\)

\(A=\frac{2.3.4.....2015}{2.3.4.....2015}.\frac{1}{2016}\)

\(A=\frac{1}{2016}\)

Vậy \(A=\frac{1}{2016}\)

Chúc bạn học tốt ~ 

\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)..\left(1-\frac{1}{2016}\right)\)

\(\Rightarrow A=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{2015}{2016}\)

\(\Rightarrow A=\frac{1.2.3..2015}{2.3.4..2016}\)

\(\Rightarrow A=\frac{1}{2016}\)

k đúng cho mk nha

\(A=\left(-\frac{1}{2}\right).\left(-\frac{2}{3}\right).\left(-\frac{3}{4}\right)......\left(-\frac{2013}{2014}\right)=\left(-\frac{1}{2014}\right)\) (Do các thừa số đều âm và A có (2014-2)+1=2013 thừa số nên A mang giá trị âm)

\(B=-\frac{1}{2015}\)

=> A<B (|A|>|B|)

Câu A mình làm được nhưng dài quá

B=\(\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).............\left(1+\frac{1}{2015}\right)\)

=\(\frac{3}{2}.\frac{4}{3}..............\frac{2016}{2015}\)

=\(\frac{3.4...............2016}{2.3................2015}\)

=\(\frac{2016}{2}=1008\)

=(-1/2) : (-2/3) :( -3/4) :...: (-49/50) 

= -1/2 . (-3/2) . (-4/3) . ... . (-50/49)

= -1/2.(-1/2) . (-50)

= - 1/100

mik ko bik viết kiểu của bn nên khó nhìn, thông cảm nha

à nhầm 

(1/2 -1) : ( 1/3-1) : ( 1/4 -1) : ... : ( 1/50 - 1) = -1/2 : -2/3 : -3/4 : ... : -49/50 

= -1/2 . (-3/2) . ( -4/3) . ... . (-50/49)

= -( 1/2.1/2 . 50)

= -25/2

= 

TA CÓ

y=1/2.2/3.3/4..............2013/2014.2014/2015

y=(1.2.3...............2014)/(2.3.4..............2015)

y=1/2015

=\(\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x...x\frac{2013}{2014}x\frac{2014}{2015}\)

=\(\frac{1x2x3x...x2013x2014}{2x3x4x...x2014x2015}\)

=\(\frac{1}{2015}\)

( Dau x la dau nhan)

\(\frac{2}{2015}\)

1/2015 dung day minh lam roi