`S= 1 -1/2 + 1/3 -1/4 +...+ 1/2011 - 1/2012 + 1/2013`
`S= (1+1/3 +...+1/2011 +1/2013) - (1/2 + 1/4+...+1/2012)`
`S= 1+1/2 + 1/3 +1/4 +....+1/2011 + 1/2012+1/2013 - 2(1/2 + 1/4+...+1/2012)`
`S= 1+ 1/2 +1/3 +1/4 +...+1/2012 +1/2012 -1 -1/2 -...-1/1006`
`S= 1/1007 + 1/1008 + 1/1009 +...+ 1/2012 = P`
Vì `S=P`
`=> S-P = 0 `
`=> (S-P)^2013 = 0`
Vậy `(S-P)^2013 =0`