Question

[Nguyễn Mạnh Quân]

S = 1-1/2+1/3-1/4+...+1/2011-1/2012+1/2013

P = 1/2007+1/2008+1/2009+...+1/2012+1/2013

Tính ( S - P )^2013

Answer 1

[Nhóc_Siêu Phàm]

S-P= (1 - 1/2 + 1/3 - 1/4 +...+ 1/2011 - 1/2012 + 1/2013) - ( 1/1007 + 1/1008 +...+ 1/2012 + 1/2013 )
 S-P= (1- 1/2 + ... + 1/1005 - 1/1006) - 2.(1/1008 + 1/1010 + 1/1012 +...+ 1/2012)
 S-P= 1+1/2+1/3+...+1/1006 - 2.( 1/2 + 1/4 + 1/6 +...+ 1/2012)
 S-P= 1 + 1/2 + 1/3 +...+ 1/1006 - ( 1+ 1/2 + 1/3 +...+ 1/1006 )
 S-P= 0
⇒ (S-P)^2013 = 0