2^(n+1)/[2^n+1] = 2/[1+(1/2)^n],
lim_{ n→∞ } (1/2)^n = 0,
所以
lim_{ n→∞ } 2^(n+1)/[2^n+1] = lim_{ n→∞ } 2/[1+(1/2)^n] = 2/[1+0] = 2
请教大大们个关于数列极限的问题.lim n→∞ 2的n+1次方除以2的n次方+1,请问这题的数列极限?
2^(n+1)/[2^n+1] = 2/[1+(1/2)^n],
lim_{ n→∞ } (1/2)^n = 0,
所以
lim_{ n→∞ } 2^(n+1)/[2^n+1] = lim_{ n→∞ } 2/[1+(1/2)^n] = 2/[1+0] = 2