Question

Determine whether the sequence converges or diverges. If it converges, give the limit. 108, -54, 27, -27/2

Answer 1

Hello,

a(1)=108
a(2)=a(1)/(-2)=-54
a(3)=a(2)/(-2)=a(1)/(-2)²=27
a(4)=a(3)/(-2)=a(1)/((-2)^3)=-27/2


a(n)=a(1)/(-2)^(n-1)=108 *(-1/2)^(n-1) (exponential decreasing)

lim if x->infinite (a(n))=0==> converges