a.Đề bài

=1/2 x 2/3 x 3/4  x...x 9/10

rút gọn

= 1-1/10 
= 9/10

k mình nha học tốt

các bạn giúp mình nhanh nhanh với

a, \(A=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}}{\frac{2011}{1}+\frac{2010}{2}+\frac{2009}{3}+...+\frac{1}{2011}}\)

\(A=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}}{\left(\frac{2011}{1}+1\right)+\left(\frac{2010}{2}+1\right)+\left(\frac{2009}{3}+1\right)+...+\left(\frac{1}{2011}+1\right)+1}\)

\(A=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}}{\frac{2012}{1}+\frac{2012}{2}+\frac{2012}{3}+...+\frac{2012}{2011}+\frac{2012}{2012}}\)

\(A=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}}{2012\cdot\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}+\frac{1}{2012}\right)}=\frac{1}{2012}\)

b, \(\frac{A}{B}=\frac{\frac{1}{2}+\frac{1}{3}+....+\frac{1}{2016}+\frac{1}{2017}}{\frac{2016}{1}+\frac{2015}{2}+\frac{2014}{3}+...+\frac{2}{2015}+\frac{1}{2016}}\)

\(\frac{A}{B}=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2016}+\frac{1}{2017}}{\left(\frac{2016}{1}+1\right)+\left(\frac{2015}{2}+1\right)+\left(\frac{2014}{3}+1\right)+...+\left(\frac{2}{2015}+1\right)+\left(\frac{1}{2016}+1\right)+1}\)

\(\frac{A}{B}=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2017}}{\frac{2017}{1}+\frac{2017}{2}+\frac{2017}{3}+...+\frac{2017}{2015}+\frac{2017}{2016}+\frac{2017}{2017}}\)

\(\frac{A}{B}=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2017}}{2017\cdot\left(\frac{1}{2}+\frac{1}{3}+....+\frac{1}{2015}+\frac{1}{2016}+\frac{1}{2017}\right)}=\frac{1}{2017}\)

A=\(-\frac{2392}{19809}\)

đẹp tk nha

-2392/19809

1/

A= 1/15+1/35+1/63+1/99+ ... + 1/9999

A=1/3.5+1/5.7+1/7.9+ ... +1/99.101

2A=2/3.5+2/5.7+2/7.9+ ... +2/99.101

2A=1/3-1/5+1/5-1/7+1/7-1/9+ ... + 1/99-1/101

2A=1/3-1/101

A=49/303

Sai thì thôi nhé

A= 1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7

A=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7

A=1-1/7

A=6/7

     bn ơi sai đề r bn ơi cái 1/52 phải là 1/56 chứ

A= đã cho.

=>-A=1/20+1/30+1/42+1/56+1/72+1/90+1/110.

=>-A=1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10+1/10*11.

=>-A=1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11.

=>-A=1/4-1/11=7/44.

=>A=-7/44.

thay số 1/52 là 1/56 mới đúng,mk làm rồi.

tk mk nha các bn.

-chúc ai tk mk học giỏi-

sai đề mất rồi 

* Cách làm : Tử giữ nguyên,còn mẫu ta biến đổi như sau:
Mẫu : ( \(\frac{19}{1}\)+ 1 ) + ( \(\frac{18}{2}\)+ 1 ) + ( \(\frac{17}{3}\)+ 1 ) +...+ ( \(\frac{3}{17}\)+ 1 ) + ( \(\frac{2}{18}\)+ 1 ) + ( \(\frac{1}{19}\)+ 1 ) - 19  ( vì ta cộng với 19 số 1 nên phải trừ 19 )
= \(\frac{20}{1}\)+  \(\frac{20}{2}\)+  \(\frac{20}{3}\)+...+  \(\frac{20}{17}\)+  \(\frac{20}{18}\)+  \(\frac{20}{19}\)- 19
=  \(\frac{20}{2}\)+  \(\frac{20}{3}\)+...+  \(\frac{20}{17}\)+   \(\frac{20}{18}\)+  \(\frac{20}{19}\)+ ( \(\frac{20}{1}\)- 19)
=  \(\frac{20}{2}\)+  \(\frac{20}{3}\)+ ...+   \(\frac{20}{17}\)+  \(\frac{20}{18}\)+  \(\frac{20}{19}\)+  \(\frac{20}{20}\)
= 20.( \(\frac{1}{2}\)+  \(\frac{1}{3}\)+...+  \(\frac{1}{17}\)+  \(\frac{1}{18}\)+  \(\frac{1}{19}\)+  \(\frac{1}{20}\))
=> \(\frac{Tử}{Mâu}\)=  \(\frac{1}{20}\)

Phùng Quang Thịnh biến đổi sai 1 chỗ kìa 

-19 = \(\frac{20}{20}-20\)chứ mà bạn

thank Lê Tài Bảo Châu nhá

\(A=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}\)

\(A=\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}+\frac{1}{10\cdot11}+\frac{1}{11\cdot12}\)

\(A=\frac{1}{5}+\frac{1}{6}-\frac{1}{6}+\frac{1}{5}...+\frac{1}{11}-\frac{1}{12}\)

\(A=\frac{1}{5}-\frac{1}{12}\)

\(A=\frac{7}{60}\)

A = \(\frac{1}{5.6}+\frac{1}{6.7}+...+\)\(\frac{1}{10.11}+\frac{1}{11.12}\)

A = \(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\)\(\frac{1}{11}-\frac{1}{12}\)

A = \(\frac{1}{5}-\frac{1}{12}\)

A = \(\frac{7}{60}\)

dễ đúng không