求这个数列的极限lim下面是n→∞ ∑上面是n下面是k=0(1/2)^k

Question

求这个数列的极限lim下面是n→∞ ∑上面是n下面是k=0(1/2)^k

Answer 1

lim下面是n→∞ ∑上面是n下面是k=0(1/2)^k
=lim(1+1/2+1/2^2+.+1/2^n)
=lim(1-1/2^(n+1))/(1-1/2)
=1/(1-1/2)
=2
(因为lim1/2^(n+1)=0)