Question

`lim_(x rightarrow ∞) sum_(x = 1)^20 cos^(2n) (x - 10)` is equal to ______.

Options

• 0

• 1

• 19

• 20

Answer 1

`lim_(x rightarrow ∞) sum_(x = 1)^20 cos^(2n) (x - 10)` is equal to 1.

Explanation:

∵ `lim_(n rightarrow ∞) cos^(2n) x = {{:(1",", x = r  π",", r ∈ I),(0",", x ≠ r  π",", r ∈ I):}`

Here, for x = 10, `lim_(x rightarrow ∞) cos^(2n) (x - 10)` = 1

and in all other cases, it is zero.

∴ `lim_(n rightarrow ∞) sum_(x = 1)^20 cos^(2n) (x - 10)` = 1