\(\dfrac{1}{10}A=\dfrac{10^{2012}+1}{10^{2012}+10}=1-\dfrac{9}{10^{2012}+10}\)

\(\dfrac{1}{10}B=\dfrac{10^{2011}+1}{10^{2011}+10}=1-\dfrac{9}{10^{2011}+10}\)

10^2012+10>10^2011+10

=>9/10^2012+10<9/10^2011+10

=>-9/10^2012+10>-9/10^2011+10

=>A>B

Sửa đề: Chứng mình chia hết 24

Tách: 24=8.3

A=102012+102011+102010+102009+8A=102012+102011+102010+102009+8

⇒$A=\mathrm{10...08}$$⋮$3 (1)

$A=\mathrm{10...008}⋮$8 (Vì: 008$⋮$8) (2)

Từ (1) và (2) ⇒A$⋮$24 Vì: (3,8)

⇒đpcm

tham khảo

https://olm.vn/hoi-dap/detail/48844794829.html

A=10 ²⁰¹²+10 ²⁰¹¹+10 ²⁰¹⁰+10 ²⁰⁰⁹+8

  = 100..0 + 100...0 + 100...0 + 100...0 +8

(2012 số 0) (2011 số 0) (2010 số 0) (2009 số 0)

  = (1+0+0+...+0)+(1+0+0+...+0)+(1+0+0+...+0)+(1+0+0+...+0)+8

  =12

11/2 bn nhé

mình làm trên violympic rui ra 11/2

\(S=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2010.2011}\)

\(S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2010}-\frac{1}{2011}\)

\(S=1-\frac{1}{2011}\)

\(S=\frac{2010}{2011}\)

Phân tích: 1 / 1 x 2 = 1 - 1/2

1/2.3 = 1/2 - 1/3

. ....Bạn làm tương tự các số còn lại...

Ta được: 1 - 1/2 + 1/2 - 1/3 + ....+1/ 2010 - 1/2011

= 1 - 1/2011

= 2010/2011

Đặt S = 1 x 2 + 2 x 3 + ......... + 99 x100

3S = 1 x 2 x 3 + 2 x 3 x (4 - 1) + ...... + 99 x 100 x (101 - 98)

3S = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + ...... + 99 x 100 x 101 - 98 x 99 x 100

3S = ( 1 x 2 x 3 - 1 x 2 x 3)  +.... + (98 x 99 x 100 - 98 x 99 x 100) + 99 x 100 x 101

3S = 99 x 100 x 101

S = 99 x 100 x 101 : 3 = 333300

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2005.2006}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2005}-\frac{1}{2006}\)

\(=1-\frac{1}{2006}\)

\(=\frac{2005}{2006}\)

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2005.2006}\)

= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2005}-\frac{1}{2006}\)

= \(1-\frac{1}{2006}\)

= \(\frac{2005}{2006}\)

\(\frac{1}{1}\cdot2=2\)

\(\frac{1}{2}\cdot3=\frac{3}{2}\)

sao mai van trua co ngoui cha loi