(1)
an=4^(4-n)=16/4^n
a(n+1)/an=4^n/4^(n+1)=1/4,首项a1=64,不等于0,数列为等比数列.
Sn=64*[1-(1/4)^n]/(1-1/4)=(256/3)(4^n-1)/(4^n)=256/3-256/(3*4^n)
n趋向于无穷大时,256/(3*4^n)趋向于0
Sn极限=256/3
(2)
a(n+1)=an*(-1/3),首项81不等于0,数列为等比数列.
Sn=81*[1-(-1/3)^n]/(1-1/3)=(243/2)[(3^n-1)/3^n]=243/2-243/(2*3^n)
n趋向于无穷大时,243/(2*3^n)趋向于0
Sn极限=243/2
两题类型一样的.