Ta có: \(\dfrac{1}{1\cdot5}+\dfrac{1}{5\cdot10}+...+\dfrac{1}{2010\cdot2015}\)

\(=\dfrac{1}{5}+\dfrac{1}{5}\left(\dfrac{5}{5\cdot10}+\dfrac{5}{10\cdot15}+...+\dfrac{5}{2010\cdot2015}\right)\)

\(=\dfrac{1}{5}+\dfrac{1}{5}\left(\dfrac{1}{5}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{15}+...+\dfrac{1}{2010}-\dfrac{1}{2015}\right)\)

\(=\dfrac{1}{5}+\dfrac{1}{5}\left(\dfrac{1}{5}-\dfrac{1}{2015}\right)\)

\(=\dfrac{1}{5}+\dfrac{1}{5}\cdot\dfrac{402}{2015}\)

\(=\dfrac{1}{5}\left(1+\dfrac{402}{2015}\right)\)

\(=\dfrac{1}{5}\cdot\dfrac{2417}{2015}=\dfrac{2417}{10075}\)

\(B=\dfrac{1}{4}\times\left(\dfrac{4}{1\times5}+\dfrac{4}{5\times9}+\dfrac{4}{9\times13}+...+\dfrac{4}{125\times129}\right)\)

\(=\dfrac{1}{4}\times\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{125}-\dfrac{1}{129}\right)\)

\(=\dfrac{1}{4}\times\left(1-\dfrac{1}{129}\right)=\dfrac{1}{4}\times\dfrac{128}{129}=\dfrac{32}{129}\)

cao phan tuấn anh : ko làm mà mơ đc tick

\(D=\dfrac{1}{1\cdot5}+\dfrac{1}{5\cdot9}+...+\dfrac{1}{21\cdot25}\)

\(4D=\dfrac{4}{1\cdot5}+\dfrac{4}{5\cdot9}+...+\dfrac{4}{21\cdot25}\)

\(4D=1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{21}-\dfrac{1}{25}\)

\(4D=1-\dfrac{1}{25}=\dfrac{24}{25}\)

\(D=\dfrac{24}{25}\cdot\dfrac{1}{4}=\dfrac{4\cdot6}{25\cdot4}=\dfrac{6}{25}\)

\(\dfrac{1}{1\times5}+\dfrac{1}{5\times9}+...+\dfrac{1}{45\times49}\)

\(=\dfrac{1}{4}\times\left(\dfrac{4}{1\times5}+\dfrac{4}{5\times9}+...+\dfrac{4}{45\times49}\right)\)

\(=\dfrac{1}{4}\times\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{45}-\dfrac{1}{49}\right)\)

\(=\dfrac{1}{4}\times\left(1-\dfrac{1}{49}\right)=\dfrac{1}{4}\times\dfrac{48}{49}=\dfrac{12}{49}\)

=21 nha

Ta có

kết quả là:

= 21

nha bn 

~**** nha~

Bạn nào đúng nhất và nhanh nhất mình k nha

Nhanh nha mình cần gấp 

ghi cả cách trình bày ra nhé

1 + 1 x 5 : 5 

= 1 + 1 x 5 : 5

= 1 + 1 x 1

= 1 + 1

= 2

= 1+5:5

=1+1

=2

1+1x5:5=1+5:5=1+1=2