Question

\(A=\frac{1\cdot2}{2\cdot2}\cdot\frac{2\cdot3}{3\cdot3}\cdot\frac{3\cdot4}{4\cdot4}\cdot\frac{4\cdot5}{5\cdot5}\cdot.................\cdot\frac{2012\cdot2013}{2013\cdot2013}\)với

\(B=\frac{2012\cdot2013-2012\cdot2012}{2012\cdot2011+2012\cdot2}\)

Answer 1

So sánh à bạn?

Answer 2

A=\(\frac{1}{2}\).\(\frac{2}{3}\)....\(\frac{2012}{2013}\)=\(\frac{1}{2013}\)

B=\(\frac{2012}{2012.2013}\)=\(\frac{1}{2013}\)

vậy A=B

Answer 3

\(A=\frac{1.2}{2.2}.\frac{2.3}{3.3}.\frac{3.4}{4.4}.\frac{4.5}{5.5}.....\frac{2012.2013}{2013.2013}=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}....\frac{2012}{2013}=\frac{1.2.3.4.5....2012}{2.3.4.5....2013}=\frac{1}{2013}\)

\(B=\frac{2012.2013-2012.2012}{2012.2011+2012.2}=\frac{2012.\left(2013-2012\right)}{2012.\left(2011+2\right)}=\frac{2012}{2012.2013}=\frac{1}{2013}\)

\(\Rightarrow A=B\)

Answer 4

\(A=\frac{1.2}{2.2}.\frac{2.3}{3.3}.\frac{3.4}{4.4}.....\frac{2012.2013}{2013.2013}\)

\(A=\frac{1.2.2.3.3.4.....2012.2013}{2.2.3.3.4.4.....2013.2013}\)

\(A=\frac{1}{2013}\)

\(B=\frac{2012.2013-2012.2012}{2012.2011+2012.2}\)

\(B=\frac{2012.\left(2013-2012\right)}{2012.\left(2011+2\right)}\)

\(B=\frac{1}{2013}\)

b không ghi đề bài nên mk chỉ có thể giúp b tính A,B thôi

Answer 5

\(A=\frac{\left(1.2.3...2012\right).\left(2.3.4.5...2013\right)}{\left(2.3.4.5...2013\right).\left(2.3.4.5...2013\right)}\)

\(A=\frac{1}{2013}\)

\(B=\frac{2012.2013-2012.2012}{2012.2011+2012.2}\)

\(B=\frac{2012.\left(2013-2012\right)}{2012.\left(2011+2\right)}\)

\(B=\frac{2012.1}{2012.2013}\)

\(B=\frac{1}{2013}\)

\(\)Nếu đề bài là so sanh thì đây:

Vì \(\frac{1}{2013}=\frac{1}{2013}\)

\(=>A=B\)