lim [(a_1)+(a_2+…+(a_n)^(1/r))^(1/r)]^(1/r) from n=1 to n→∞的敛散性的讨论

The discussion of the convergence and divergence of lim [(a_1)+(a_2+…+(a_n)^(1/r))^(1/r)]^(1/r) from n=1 to n→∞

从数列[2+(2+…+2^(1/2))^(1/2)]^(1/2)到一般形式的数列[(a_1)+(a_2+…+(a_n)^(1/2))^(1/2)]^(1/2),再到更一般形式的数列[(a_1)+(a_2+…+(a_n)^(1/r))^(1/r)]^(1/r),并对其敛散性作出讨论。

From sequence of numbers{√2＋√2＋…＋√2}to a genera… from{√a1＋√a2＋…＋√an}and to a more genera…from{r√a1＋r√a2＋…＋r√an}, discuss about the convergence and divergence of it.