Limiting cos at infinity

Calculus Level 4

Evaluate the following limit

lim ⁡ n → ∞ ∑ x = 1 1729 cos ⁡ 2 n ( x − 10 ) \displaystyle\lim_{n \rightarrow \infty} \sum_{x=1}^{1729} \cos^{2n}(x-10) where n n is an integer .

Enter 999 if you think the limit does not exist.


The answer is 1.

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1 solution

Kushal Bose
Jan 1, 2017

If x = 10 x=10 then value of cosine is 1 1 .

If x ≠ 10 x \neq 10 then value of cosine is a positive fraction .When a positive fraction is raised to a infinite power then it tends to zero.

So, rest of the terms are zero only one term is 1 1

0 Helpful 0 Interesting 0 Brilliant 0 Confused

You mean cos^2 is a positive fraction. And that raised to infinity tends to 0. Cosine would oscillate from negative to positive as we move further through the radians

Arghyadeep Chatterjee - 3 years ago

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