A limit of sum !

Calculus Level 4

Evaluate lim ⁡ n → ∞ ( ∑ i = 1 i = n i csc ⁡ 2 x ) sin ⁡ 2 x \lim_{n \to \infty} \left( \sum_{i=1}^{i=n} i^{\csc^{2}x} \right) ^{\sin^{2}x} can be expressed as n α n^{\alpha} what is the value of α \alpha ?

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The answer is 1.

Abhishek Singh by Abhishek Singh , 24, India

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2 solutions

Antara Chatterjee
May 24, 2018

x should also tend to 0 for the limit to be equal to n. this problem is incomplete.

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Gautam Sachdeva
Jun 4, 2017

cosec^2(x)*sin^2(x)=1which is in power. The exp can be made of 1+2+3+4+....+n All have power 1.

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