lim n → ∞ 20 ∑ x = 1 c o s 2 n ( x − 10 ) is equal to Options: A . &nbsp 0 B . &nbsp 1 C . &nbsp 19 D . &nbsp 20

Answer: Option B : B lim n → ∞ c o s 2 n x = { 1 , x = r π , r ∈ I 0 , x ≠ r π , r ∈ I Here, for x = 10, lim n → ∞ c o s 2 n ( x − 10 ) = 1 and in all other cases it is zero ∴ lim n → ∞ 20 ∑ x = 1 c o s 2 n ( x − 10 ) = 1

limn→∞ 20∑x=1 cos 2n(x−10) is equal to

Discussion Forum : Limits Continuity And Differentiability

Question -

$lim n \to \infty$ $20 \sum x = 1$ $c o s^{2 n} (x - 10)$ is equal to

Options:

A . 0

B . 1

C . 19

D . 20

Answer: Option B
:
B

$lim n \to \infty$ $c o s^{2 n}$ $x$ = ${\begin{matrix} 1, x = r π, r \in I 0, x \neq r π, r \in I \end{matrix}$

Here, for $x$ = 10, $lim n \to \infty c o s^{2 n} (x - 10)$ = 1

and in all other cases it is zero

$∴ lim n \to \infty 20 \sum x = 1 c o s^{2 n} (x - 10)$ = 1

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Discussion Forum : Limits Continuity And Differentiability

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