求极限lim(n趋于无穷大)(a +a^2 +a^3+ ...+ a^n)/(2 +2^2+ ...+2^n)(a>0,a不等于1)
问题描述:
求极限lim(n趋于无穷大)(a +a^2 +a^3+ ...+ a^n)/(2 +2^2+ ...+2^n)(a>0,a不等于1)
答
a +a^2 +a^3+ ...+ a^n = a(1 - a^n)/1-a2 +2^2+ ...+2^n = 2(1 - 2^n)/(1 - 2) = 2^(n+1) - 20