Limit with trigonometric sums

[Guest]

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

[Guest]

[tex]\frac{2n+1}{6}[/tex]

Use l'hopital's rule twice,
https://www.google.co.uk/url?sa=t&rct=j ... v5YkwxWyVw

or alternatively

Taylor expand all the functions and keep track of terms [tex]1[/tex], [tex]x[/tex], [tex]x^2[/tex], and ignore higher order terms.

Hope this helped,

R. Baber.