极限题lim(1+1/2+1/4+.+1/2^n) n→无穷lim((x^2 -1)/(x^2 +3))^(x^2 +1

学习时间:2026-04-03 13:47:28 阅读：3928

极限题lim(1+1/2+1/4+.+1/2^n) n→无穷lim((x^2 -1)/(x^2 +3))^(x^2 +1) 这个题x^2跟后面加的数字都是分开的x→无穷这2个题的过程怎么写啊?

爱听歌的山水

2026-04-03 13:47:28

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1。设s=1+1/2+1/4+…+1/2^n=1*(1-(1/2)^(n+1))/(1-(1/2))=2*(1-(1/2)^(n+1))当n->无穷时,(1/2)^(n+1)=0∴lims=22。原式=lim(1-1/x^2)/(x^2+3)(1+1/x^2)=lim1/(x^2+3)=0