Sequence limit Lim [(1 & # 178; + 2 & # 178; + 3 & # 178; +...] +N & # 178;) / N & # 179;] (n - > ∞), why is it equal to 1 / 3 I know that the correct solution is to decompose the general term of the molecule, then divide it by the denominator n & #, and finally equal to 1 / 3 What I want to ask is, what's wrong with thinking like this? The original Lim [(1 & # 178; + 2 & # 178; + 3 & # 178; +...] +n²)/n³] = lim （1/n³+2/n³+3/n³+… +n²/n³） = lim（0+0+0+… +0） = 0 In addition, Molecules 1 and 178; + 2 and 178; + 3 and 178; + +N &# 178; and denominator n &# 179;, both of which have no limit, are division operations of two infinite sequences, If we regard the part of n &# as 1 / N &# then there is a limit for 1 / N &# i.e "The original formula is an infinite sequence of numbers 1 & # 178; + 2 & # 178; + 3 & # 178; +..." +"The product of N & # 178;, and 1 / N & # 179;" Can you see that? Why not?

Sequence limit Lim [(1 & # 178; + 2 & # 178; + 3 & # 178; +...] +N & # 178;) / N & # 179;] (n - > ∞), why is it equal to 1 / 3 I know that the correct solution is to decompose the general term of the molecule, then divide it by the denominator n & #, and finally equal to 1 / 3 What I want to ask is, what's wrong with thinking like this? The original Lim [(1 & # 178; + 2 & # 178; + 3 & # 178; +...] +n²)/n³] = lim （1/n³+2/n³+3/n³+… +n²/n³） = lim（0+0+0+… +0） = 0 In addition, Molecules 1 and 178; + 2 and 178; + 3 and 178; + +N &# 178; and denominator n &# 179;, both of which have no limit, are division operations of two infinite sequences, If we regard the part of n &# as 1 / N &# then there is a limit for 1 / N &# i.e "The original formula is an infinite sequence of numbers 1 & # 178; + 2 & # 178; + 3 & # 178; +..." +"The product of N & # 178;, and 1 / N & # 179;" Can you see that? Why not?

Dizzy, how can you do that
Molecules should be summed first
1²+2²+3²+ … +n²
=n(n+1)(2n+1)/6
Then look at the highest degree coefficient 1 / 3
So the limit is 1 / 3