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NTA Abhyas JEE Main2020MathematicsLimitsPractice

The value of lim x → π 2 ⁡ 1 1 cos 2 ⁡ x + 2 1 cos 2 ⁡ x + . … … … + 10 1 cos 2 ⁡ x cos 2 ⁡ x is equal to

Correct answer

10

Step-by-step solution

Let, L = lim x → π 2 ⁡ 1 1 cos 2 ⁡ x + 2 1 cos 2 ⁡ x + . … … … + 10 1 cos 2 ⁡ x cos 2 ⁡ x Putting 1 cos 2 ⁡ x = y , we get, L = lim y → ∞ ⁡ 1 y + 2 y + . … … . + 10 y 1 y = l i m y → ∞ 10 1 10 y + 2 10 y + . … … . + 10 10 y 1 y = 10 0 + 0 + . … … + 1 0 = 10

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