Question

Thực hiện phép tính:

1/1.2.3 + 1/2.3.4 + 1/3.4.5 +......+ 1/2007.2008.2009

làm ơn giúp tớ với !!!!!!!!

Answer 1

1/1.2.3+1/2.3.4+...+1/2007.2008.2009=1-1/2-1/3+1/2-1/3-1/4+...-1/2008-1/2009=1-1/2009=2008/2009

Answer 2

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+.....+\frac{1}{2007.2008.2009}\)

\(=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-.....-\frac{1}{2008.2009}\)

\(=\frac{1}{1.2}-\frac{1}{2008.2009}=\frac{1}{2}-\frac{1}{4034072}=\frac{2017035}{4034072}\)