lim(1/n+2^1/n)^n n→∞求详解!高数极限

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lim(1/n+2^1/n)^nn→∞求详解!高数极限lim(1/n+2^1/n)^nn→∞求详解!高数极限lim(1/n+2^1/n)^nn→∞求详解!高数极限答案目测是:e重要极限的变形,(1+1

lim(1/n+2^1/n)^n n→∞求详解!高数极限
lim(1/n+2^1/n)^n n→∞求详解!高数极限

lim(1/n+2^1/n)^n n→∞求详解!高数极限


答案目测是:e
重要极限的变形,(1+1/n)^n =e n趋于无穷时

=lim[1+(1/n+2^1/n-1﹚]^[1/(1/n+2^1/n-1﹚][(1/n+2^1/n-1﹚]n
∵lim(1/n+2^1/n-1﹚n=lim[﹙1+ln2﹚/n]n=1+ln2
∴原式极限=e^﹙1+ln2﹚=2e