an= -2[n-(-1/2)^n]
= -2n+(-1/2)^(n-1)
sn=a1+a2+.+an
= -2*1+(-1/2)^(1-1) -2*2+(-1/2)^(2-1)-.- 2n+(-1/2)^(n-1)
= -2*(1+2+.+n)+(-1/2)^0 -2*2+(-1/2)^1+.+(-1/2)^(n-1)
= -n(n+1)+[1-(-1/2)^n]/[1-(-1/2)]
= -n(n+1)+[1-(-1/2)^n]/[3/2]
= -n(n+1)+2[1-(-1/2)^n]/3
= -n(n+1)+[2-(-1/2)^(n-1)]/3
= -n(n+1)-(-1/2)^(n-1)/3+2/3
s10
= -10*(10+1)-(-1/2)^(10-1)/3+2/3
= -110-(-1/2)^9/3+2/3
= -110+(1/512)/3+2/3
= -110+1/1536+1024/1536
= -110+1025/1536
= -109-511/1536
= -109又511/1536