Jika diketahui bahwa x = 1 / 2013 - 2 / 2013 + 3 / 2013 - 4 / 2013 + ... - 2012 / 2013, nilai x yang memenuhi adalah ... Matdas simak UI 2013

.
misal
x = p - q
p = 1/2013 +....+ 2011/2013
p = 1/2013 (  1 + 3 + 5 + ..+2011)
1,3,5,...,2011
a =1 , b = 2 , un = 2011 --> n = 1/2 (2011+1) = 1006
sn = n/2 (a + un)
sn = 1006/2 ( 1 + 2011)

p = 1/2013  { 1006/2 (2012)}
.
q =  2/2013  + 4/2013 + 6/2013 + ...+ 2012/2013
q = 1/2013  (2 +4 +6 + ...+2012)
2+4 +6 + ...+2012=
a = 2 , b = 2 , un = 2012
n = 2012/2 = 1006
sn = 1006/2 ( 2 + 2012)
q = 1/2013 { 1006/2 ( 2014)}
.
x=  p - q
x = { 1/2013 (1006/2) (2012 ) - 1/2013 (1006/2) (2014)}
x = 1/2013 . 1006/2 (2012 - 2014)
x= 1/2013. 10006/2. (-2)
x = - 1006/2013