lim(n趋近于无穷大）1/n∑(i=1到n)(1+i/n)∧(1/3)用定积分做.--!可不可以把第一步写清楚点

Question

lim(n趋近于无穷大）1/n∑(i=1到n)(1+i/n)∧(1/3) 用定积分做.
-_-!可不可以把第一步写清楚点

Answer 1

lim(n→∞) (1/n) Σ(i=1→n) (1 + i/n)^(1/3)
= ∫[1→2] x^(1/3) dx
= x^(1 + 1/3)/(1 + 1/3) |[1→2]
= (3/4)x^(4/3) |[1→2]
= (3/4)2^(4/3) - (3/4)(1)
= 3/2^(2/3) - 3/4