Question

TÍNH:

\(\frac{1}{1x3}\)+\(\frac{1}{3x5}\)+\(\frac{1}{5x7}\)+....+\(\frac{1}{2009x2011}\)

GIÚP MINK NHA, THANKS, AI NHANH SẼ TICK

Answer 1

Tớ không chép lại đề nữa nhé:

=\(\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+....+\frac{2}{2009.2011}\right)\)=\(\frac{1}{2}.\left(\frac{3-1}{1-3}+\frac{7-5}{5-7}+...+\frac{2011-2009}{2009-2011}\right)\)

= \(\frac{1}{2}.\left(\frac{3}{1.3}-\frac{1}{1.3}+\frac{5}{3.5}-\frac{3}{3.5}+...+\frac{2011}{2009.2011}-\frac{2009}{2009.2011}\right)\)

=\(\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{2009}-\frac{1}{2011}\right)\)

=\(\frac{1}{2}.\left(1-\frac{1}{2011}\right)\)

=\(\frac{1}{2}.\frac{2010}{2011}\)

=\(\frac{1005}{2011}\)

Answer 2

bạn ơi đó là dấu nhân hay chữ ''x'' vậy?

Answer 3

nếu là dấu nhân thì như sau:

\(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+...+\frac{1}{2009\cdot2011}=1\cdot\frac{1}{3}+\frac{1}{3}\cdot\frac{1}{5}+...+\frac{1}{2009}\cdot\frac{1}{2011}=1\cdot\frac{1}{2011}=\frac{1}{2011}\)

CHẮC LÀ ĐÚNG ĐÓ BẠN. NHỚ K VÀ KB VS MK NHA. CHÚC BẠN HỌC TỐT. -_-

Answer 4

\(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{2009\cdot2011}\)

\(=\frac{1}{2}\cdot\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2009}-\frac{1}{2011}\right)\)

\(=\frac{1}{2}\cdot\left(1-\frac{1}{2011}\right)\)

\(=\frac{1}{2}\cdot\frac{2010}{2011}\)

\(=\frac{1005}{2011}\)

k cho mình nhé