Question

[Nguyễn Huệ Lam]

Thuc hien phep tinh: 

\(P=\left(1-\frac{1}{1+2}\right).\left(1-\frac{1}{1+2+3}\right)...\left(1-\frac{1}{1+2+3+4+...+2011}\right)\)

Ai trả lời nhanh và đúng nhất tôi sẽ tích cho. 

Answer 1

[kagamine rin len]

P=(1-1/1+2).(1-1/1+2+3)....(1-1/1+2+3+4+...+2011)

=[1-1/(2+1).2:2].[1-1/(3+1).3:2].....[1-1/(2011+1).2011:2]

=(1-2/2.3).(1-2/3.4)...(1-2/2011.2012)

=4/2.3.10/3.4....4046130/2011.2012

=1.4/2.3 .2.5/3.4 ....2010.2013/2011.2012

=1.2....2010/2.3...2011 .4.5....2013/3.4....2012

=1/2011.2013/3

=671/2011