A calculus problem by Jose Sacramento

Calculus Level 2

$\large \lim_{n\to\infty} \dfrac1n \left( \cos \dfrac\pi n + \cos \dfrac{2\pi}n + \cdots + \cos \dfrac{n\pi}n \right) = \, ?$

The answer is 0.

1 solution

Hey Mate
Sep 16, 2016

the limit as n approaches infinity is 0 for 1/n. 0 times anything is zero

What about the limit of (1/n)(n^2) as n approaches infinity? The limit of 1/n is still zero and it's multiplied by something, but the total limit is infinity. You have the right answer but your logic isn't sound.

Anthony Holm - 4 years, 9 months ago

This isn't a solution, you must improvise on it, there are more terms than $\frac{1}{n}$ , A Riemann integral definition would work here, try to edit the solution.

Aditya Narayan Sharma - 4 years, 9 months ago

A calculus problem by Jose Sacramento

The answer is 0.

1 solution

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