1/6*3+1/6*9+1/9*12+........+1/30*33

=(1/3-1/6)+(1/6-1/9)+(1/9-1/12)+........+(1/30-1/33)

=1/3-1/6+1/6-1/9+1/9-1/12+........+1/30-1/33

=1/3-1/33

=10/33

nho k cho mink nha 

CHUC BAN HOC GIOI !

Gợi ý: 18 = 3.6

           54 = 6.9

           108 = 9.12

           .............

           990 = 30.33

Gấp 3 lần R rồi dùng sai phân hữu hạn.

Tự làm tiếp nhé!!!

\(\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+....+\frac{1}{990}\)

\(=\frac{1}{3\times6}+\frac{1}{6\times9}+\frac{1}{9\times11}+....+\frac{1}{30\times30}\)

\(=\frac{1}{3}\times\left(\frac{3}{3\times6}+\frac{3}{6\times9}+....+\frac{3}{30\times33}\right)\)

\(=\frac{1}{3}\times\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+....+\frac{1}{30}-\frac{1}{33}\right)\)

\(=\frac{1}{3}\times\left(\frac{1}{3}-\frac{1}{33}\right)=\frac{1}{3}\times\frac{10}{33}=\frac{10}{99}\)

\(\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+...+\frac{1}{990}\)

\(=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+...+\frac{1}{30.33}\)

\(=\frac{1}{3}\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}+...+\frac{1}{30}-\frac{1}{33}\right)\)

\(=\frac{1}{3}\left(\frac{1}{3}-\frac{1}{33}\right)=\frac{1}{3}.\frac{10}{33}=\frac{10}{99}\)

a) \(\frac{1}{1x3}+\frac{1}{3x5}+\frac{1}{5x7}+...+\frac{1}{2007x2009}\)

\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2007}-\frac{1}{2009}\right)\)

\(=\frac{1}{2}.\left(1-\frac{1}{2009}\right)=\frac{1}{2}\cdot\frac{2008}{2009}=\frac{1004}{2009}\)

....

các bài cn lại bn lm tương tự nha

b, \(\dfrac{1}{18}+\dfrac{1}{54}+\dfrac{1}{108}+...+\dfrac{1}{990}\)

3A = \(\dfrac{1}{6}+\dfrac{1}{18}+...+\dfrac{1}{330}\)

3A-A = \(\dfrac{1}{6}-\dfrac{1}{990}\)

2A = 82/495

A =82/495 : 2 

A=41/495

c, \(\dfrac{4}{2.4}+\dfrac{4}{4.6}+\dfrac{4}{6.8}+...+\dfrac{4}{2008.2010}\)

A= \(\dfrac{4}{2}.\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+...+\dfrac{2}{2008.2010}\right)\)

A= \(\dfrac{4}{2}.\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{2008}-\dfrac{1}{2010}\right)\)

A= \(\dfrac{4}{2}.\left(\dfrac{1}{2}-\dfrac{1}{1010}\right)\)

A= \(\dfrac{4}{2}.\dfrac{252}{505}\)

A= \(\dfrac{504}{505}\)

Sao lại `-4x^2` ở cuối tkes kia?

\(=x^2\left(1-x^2\right)-4\left(1-x^2\right)\)

\(=\left(x^2-4\right)\left(1-x^2\right)\)

\(=\left(x-2\right)\left(x+2\right)\left(1-x\right)\left(1+x\right)\)

\(\frac{1}{18}\)+\(\frac{1}{54}\)+\(\frac{1}{108}\)+...+\(\frac{1}{990}\)

=\(\frac{1}{3.6}\)+\(\frac{1}{6.9}\)+\(\frac{1}{9.12}\)+...+\(\frac{1}{30.33}\)

=\(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+...+\)\(\frac{1}{30}-\frac{1}{33}\)

=\(\frac{1}{3}-\frac{1}{33}\)

=\(\frac{10}{33}\)

=1/3*6+1/6*9+1/9*12+...+1/30*33

=1/3*(1/3-1/6+1/6-1/9+...+1/30-1/33)

=1/3* (1/3-1/33)

=1/3*10/33

=10/99

dễ mà bn                                     

\(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{97\times99}+\frac{2}{99\times101}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}+\frac{1}{99}-\frac{1}{101}\)

\(=1-\frac{1}{101}\)

\(=\frac{100}{101}\)

1/100 = 0,01         2/1000 = 0,002         2001/100 = 20,01      

Học tốt!

Trả lời:

1/100 = 0,01

2/1000 = 0,002

2001/100 = 21,01

cái đó là phân số thập phân rùi mà 

TL

\(\frac{1}{100}\)= \(\frac{10}{1000}\)

\(\frac{2}{1000}\)= \(\frac{20}{10000}\)

\(\frac{2001}{100}\)=\(\frac{20010}{1000}\)

đặt A với biểu thức trên

A=\(\frac{1}{3x6}\)+\(\frac{1}{6x9}\)+......+\(\frac{1}{30x33}\)

Nhân cả 2 vế với 3 ta có

A x 3 = \(\frac{3}{3x6}\)+....+\(\frac{3}{30x33}\)

A x 3 = \(\frac{1}{3}\)-\(\frac{1}{6}\)+....+\(\frac{1}{30}\)-\(\frac{1}{33}\)

A x 3 = \(\frac{1}{3}\)-\(\frac{1}{33}\)

A x 3 = \(\frac{10}{33}\)

A = \(\frac{10}{33}\):3

A= \(\frac{10}{99}\)

cho vài k đi bà con ơi

a = 10 | 99 nhé