Question

limit question :

lim n->inf ( (a1)^n + (a2)^n + ... (ar)^n )^(1/n)

it is given a1 >a2 > ... > ar and are positive real numbers

Answer 1

in ai , i is the subscript .

Answer 2

n->inf, 1/n->0 ?

Answer 3

yes..

Answer 4

if im not overlooking ... anything power 0 = 1

Answer 5

well but its not exactly 0, its tending to 0 , precisely its a^b where a->inf and b->0
so you can;'t say 1 is the ans by that logic

Answer 6

ohk... gotcha

Answer 7

squeeze it

Answer 8

i am thinking we have to take (a1)^n common out right ?

squeezing ?

Answer 9

ar probably

Answer 10

once (a1)^n and second (ar)^n

Answer 11

after a1,

(1 + (a2/a1)^n + (a3/a1)^n ... (ar/a1)^n )^(1/n)

why ar but?

Answer 12

experiment is right just ar i think

Answer 13

\[ a_r ( 1 + (a_{r-1}/a_r)^n + O((a_{r-1}/a_r)^n )^{1/(a_{r-1}/a_r)^n * (a_{r-1}/a_r)^n/n} = a_r e^{0}=a_r \]