Question

lim

n→∞

1+a+a2+a3+…+an-1

1+b+b2+b3+…+bn-1

(1＜|a|＜|b|)=______．

Answer 1

lim

n→∞

1+a+a2+a3+…+an-1

1+b+b2+b3+…+bn-1

(1＜|a|＜|b|)
=

lim

n→∞

1 bn-1 + a bn-1 + a2 bn-1 +…+( a b )n-1

1 bn-1 + 1 bn-2 + 1 bn-3 +… +1

=0．