Question

x的绝对值小于1,求当n无穷大时(1+x)(1+x^2).(1+x^n)的极限

Answer 1

|x| limx^(2n) = 0

lim(1+x)(1+x^2).(1+x^n)

= lim (1-x)(1+x)(1+x^2).(1+x^n) /(1-x)

=lim (1-x^(2n)) / (1-x)

= 1/(1-x)