level 3
![[小乖]](/static/emoticons/u5c0fu4e56.png)
C不对，选B
2025年01月07日 02点01分
![[泪]](/static/emoticons/u6cea.png)
level 11
补充前提：{ak}为正项数列
f(n)=((a1)^n+(a2)^n+...+(ak)^n))^(1/n)
lim f(n) = lim ((a1)^n+(a2)^n+...+(ak)^n))^(1/n)
设max{a1,a2...ak}=am，
lim lim ((a1)^n+(a2)^n+...+(ak)^n))^(1/n)
=lim ((am)^n*((a1/am)^n+(a2/am)^n+...+(ak/am)^n)))^(1/n)
=am*lim ((a1/am)^n+(a2/am)^n+...+(ak/am)^n)^(1/n)
lim ((a1/am)^n+(a2/am)^n+...+(ak/am)^n)^(1/n)=1，
所以lim f(n) = lim ((a1)^n+(a2)^n+...+(ak)^n))^(1/n)=am=max{a1,a2...ak}
2025年01月07日 02点01分
4
f(n)=((a1)^n+(a2)^n+...+(ak)^n))^(1/n)
lim f(n) = lim ((a1)^n+(a2)^n+...+(ak)^n))^(1/n)
设max{a1,a2...ak}=am，
lim lim ((a1)^n+(a2)^n+...+(ak)^n))^(1/n)
=lim ((am)^n*((a1/am)^n+(a2/am)^n+...+(ak/am)^n)))^(1/n)
=am*lim ((a1/am)^n+(a2/am)^n+...+(ak/am)^n)^(1/n)
lim ((a1/am)^n+(a2/am)^n+...+(ak/am)^n)^(1/n)=1，
所以lim f(n) = lim ((a1)^n+(a2)^n+...+(ak)^n))^(1/n)=am=max{a1,a2...ak}