Find the limit Lim t approaching 0 (ln1 / T + lntant) / T

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• 1. 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?
• 2. Find the sequence {x} of the answer to an advanced number problem is bounded, LIM (n →∞) y = 0, prove LIM (n →∞) xy = 0
• 3. The proof of the first higher number: if an > 0 and lim (n →∞) a (n + 1) / a (n) = a, then LIM (an ^ (1 / N)) = a Is there a simpler proof
• 4. It is proved that if an > 0 and lim (n →∞) a (n) / a (n + 1) = l > 1, then LIM (n →∞) a (n) / a (n + 1) = l > 1 It is proved that if an > 0 and lim (n →∞) a (n) / a (n + 1) = l > 1, then LIM (n →∞) = 0
• 5. The general formula of Sn = 2n-n
• 6. Given that the sum of the first n terms of the sequence {an} is Sn = n2-2n + 3, then the general term formula of the sequence is______ ．
• 7. A1 = 1, Sn = nan-n (n-1), the general formula of an
• 8. If the nonzero vectors a and B satisfy: | B | = 1, and the angle between B and B-A is 60 degrees, the value range of | a |?
• 9. Given that the nonzero vector AB satisfies B = 1 and the angle between B and B-A is 30, then the value range of a is
• 10. It is known that the included angle of non-zero vectors a and B is 60 ° and | a | = | B | = 2. If vector C satisfies (A-C); (B-C) = 0, then | C | = 2? Is to find the value range
• 11. Find the limit, t tends to 0, Lim T / what is 1-cost equal to?
• 12. Power series 1-x + x ^ 2-x ^ 3 +... + (- 1) ^ (n-1) * x ^ (n-1) +... LXL
• 13. What is the sum of power series (n-1) x ^ n and function?
• 14. How to find the sum function of power series N = 0 to ∞Σ x ^ n / (n + 1)
• 15. 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.
• 16. 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
• 17. 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
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• 20. When n tends to infinity, how to find the limit of 1 / N ^ 3 + 2 ^ 2 / N ^ 3 +... + (n-1) ^ 2 / N ^ 3