How to calculate LIM (1 + 5 / N) ^ n

LIM (n →∞) (1 + 5 / N) ^ n if it is
lim(n→∞）（1+5/n）^n
=lim(n→∞）[（1+5/n）^(n/5 )]^5
=e^5

RELATED INFORMATIONS

1. Calculate LIM (a - 2 + a - 4 +...) +a⌒2n)/（a+a⌒2+a⌒3＋… +a⌒n） If the absolute value of a is less than 1, please explain in detail
2. Find the limit problem LIM (1 / (1 + x) + 1 / (1 + x) ^ 2 + 1 / (1 + x) ^ 3 +. 1 / (1 + x) ^ n) when n tends to infinity, what is the limit of the expression? It's better to be able to give the process of solving the problem
3. What does the calculus formula F '(x) = Lim △ x → 0 (f (x + △ x) - f (x)) / △ x mean? I'm a self learner - what's the slope.
4. How to find the sum function of power series N = 0 to ∞Σ x ^ n / (n + 1)
5. What is the sum of power series (n-1) x ^ n and function?
6. Power series 1-x + x ^ 2-x ^ 3 +... + (- 1) ^ (n-1) * x ^ (n-1) +... LXL
7. Find the limit, t tends to 0, Lim T / what is 1-cost equal to?
8. Find the limit Lim t approaching 0 (ln1 / T + lntant) / T
9. 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?
10. Find the sequence {x} of the answer to an advanced number problem is bounded, LIM (n →∞) y = 0, prove LIM (n →∞) xy = 0
11. The limit of (n + 2) ^ 3 / (n + 1) ^ 4 (when n tends to infinity)
12. When n tends to infinity, how to find the limit of 1 / N ^ 3 + 2 ^ 2 / N ^ 3 +... + (n-1) ^ 2 / N ^ 3
13. What is 1 + 3 + 5 + 7 + (2n-1) equal to
14. What is the limit of [4 * 6 * 8 *. * (2n + 2)] / [3 * 5 * 7 *. * (2n + 1)]?
15. 1/3+1/5+1/7…… 1/(2n+1) Look at the problem clearly, but you can't solve it
16. If the limit of 2n - (4N ^ 2-kn + 3) ^ 0.5 is 1, then the value of K is equal to?
17. LIM (1 / 2 + 1 / 2 ^ 2... + 1 / 2 ^ n) / (1 / 3 + 1 / 3 ^ 2... 1 / 3 ^ n) for limit LIM (1 / 2 + 1 / 2 ^ 2... + 1 / 2 ^ n) / (1 / 3 + 1 / 3 ^ 2... 1 / 3 ^ n) for limit
18. Find limit LIM (1-1 / 2 ^ 2) (1-1 / 3 ^ 2)... (1-1 / N ^ 2)=_____
19. Using function continuity to find the following limit LIM (x tends to 0) arctan2 ^ X / (Tan ^ 2 + (x + 2) ^ cosx)
20. Given that f (x) is continuous in a neighborhood of x = 0, and f (0) = 0, limx → 0f (x) 1-cosx = 2, then f (x) () A. Nondifferentiable B. differentiable, and f ′ (0) ≠ 0C. Get the maximum D. get the minimum