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## Homework Statement

Hi. My professor asked me if I know to solve this limit and I tried doing it, however I didn't get the same answer as him.

Question: What is the limit of (cos(x)*cos(2x)*cos(3x)*...*cos(nx)-1)/x^2 as x approches 0

## Homework Equations

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## The Attempt at a Solution

So to find this limit I used L'Hospital's rule.

I derived the top and bottom function and I noticed that each part of the derivative can be calculated using sin(x)/x as x ->0 =1. Then I noticed that the whole thing equals -(1^2+2^2+3^2+.....n^2)/2

However my professor said that the whole thing should equal -n(n+1)(2n+1)/2

Could somebody please find the part where I made the mistake