S6=a1+a2+...+a6=(a3-2d)+(a3-d)+...+(a3+3d)=6a3+3d=7a3
所以a3=3d,所以a1=d.
a2+a7=a1+d+a1+6d=2a1+7d=9d=1,所以a1=d=1.所以an=n
(2)bn=n*2^n
Tn=b1+b2+...+bn=1*2^1+2*2^2+3*2^3+...+n*2^n
2Tn=1*2^2+2*2^3+...+(n-1)*2^n+n*2^(n+1)
所以Tn-2Tn=-Tn=2^1+2^2+...+2^n-n*2^(n+1)=(1-n)*2^(n+1)-2
所以Tn=(n-1)*2^(n+1)+2
(3)cn=n*(n+2).1/cn=1/n*(n+2)
所以Gn=c1+c2+...+cn=1/1*3+1/2*4+...+1/n*(n+2)
=0.5*[1-1/3+1/2-1/4+...+1/n-1/(n+2)]
=0.5*[1+0.5-1/(n+1)-1/(n+2)]
=0.5*[1.5-(2n+3)/(n+1)(n+2)]
=0.75-(2n+3)/[2(n+1)(n+2)]