kx+(k+1)y-1=0
x/(1/k)+y/(1/(k+1))=1
所以
sk=1/2 *1/k(k+1)
从而
s1+s2+.+s2013
=1/2 (1/1×2+1/2×3+.+1/2013×2014)
=1/2 (1-1/2+1/2-1/3+.+1/2013-1/2014)
=1/2 (1-1/2014)
=1/2 ·2013/2014
=2013/4028
kx+(k+1)y-1=0
x/(1/k)+y/(1/(k+1))=1
所以
sk=1/2 *1/k(k+1)
从而
s1+s2+.+s2013
=1/2 (1/1×2+1/2×3+.+1/2013×2014)
=1/2 (1-1/2+1/2-1/3+.+1/2013-1/2014)
=1/2 (1-1/2014)
=1/2 ·2013/2014
=2013/4028