Limn- -x-120 cos 2nx-10 is equal to

Lim_n→∞^ cos ^2nx = 1, x = rπ , r ∈ I 0,x rπ ,r∈ I Here, for x = 10, lim_n→∞ cos^2n(x 10) = 1 and in all other cases it is zero ∴lim_n→∞∑_x=1^20 cos^2n(x 10 ...

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Byju's Answer

Standard XI

Mathematics

Algebra of Limits

limn→∞ ∑x=120...

Question

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

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Solution

The correct option is B
1

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

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

The correct option is B 1 limn→∞ cos 2nx = {1,x=rπ,r∈I0,x≠rπ,r∈I Here, for x = 10, limn→∞cos2n(x−10) = 1 and in all other cases it is zero ∴limn→∞20∑x=1cos2n(x−10) = 1

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