Tính (S-P)^2013

L

lechibachh

maloimi456 said:
Cho S= 1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2011}-\frac{1}{2012}+\frac{1}{2013}.
Và P= \frac{1}{1007}+\frac{1}{1008}+...+\frac{1}{2012}+\frac{1}{2013}.
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\Leftrightarrow S-P= (1 - 1/2 + 1/3 - 1/4 +...+ 1/2011 - 1/2012 + 1/2013) - ( 1/1007 + 1/1008 +...+ 1/2012 + 1/2013 )
\Leftrightarrow S-P= (1- 1/2 + ... + 1/1005 - 1/1006) - 2.(1/1008 + 1/1010 + 1/1012 +...+ 1/2012)
\Leftrightarrow S-P= 1+1/2+1/3+...+1/1006 - 2.( 1/2 + 1/4 + 1/6 +...+ 1/2012)
\Leftrightarrow S-P= 1 + 1/2 + 1/3 +...+ 1/1006 - ( 1+ 1/2 + 1/3 +...+ 1/1006 )
\Leftrightarrow S-P= 0
\Rightarrow (S-P)^2013 = 0
 
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