# Limit with trigonometric sums

### Limit with trigonometric sums

$\lim_{x \to 0}\frac{1-cosx*cos2x*cos3x*...*cosnx}{\sum_{k=1}^{n }sinkx^{2}}$

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### Re: Limit whit trigo

$\frac{2n+1}{6}$

Use l'hopital's rule twice,

or alternatively

Taylor expand all the functions and keep track of terms $1$, $x$, $x^2$, and ignore higher order terms.

Hope this helped,

R. Baber.

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