Rút gọn các tổng sau: S1=$\frac{1}{4\cos ^{2}\frac{a}{2}}$+ $\frac{1}{4^{2}cos^{2}\frac{a}{2^{2}}}$+...+$\frac{1}{4^{n}cos^{2}\frac{a}{2^{n}}}$
S2=$\frac{1}{\sin x.\sin2x}$+$\frac{1}{\sin2x.\sin3x}$+...+$\frac{1}{\sin nx.\sin(n+1)x}$
$S3=(1+\frac{1}{\cos x})(1+\frac{1}{\cos 2x})...(1+\frac{1}{\cos 2^{n-1}x})$
S4=$\frac{1}{\sin x}$+$\frac{1}{\sin 2x}$+...+$\frac{1}{\sin 2^{n-1}x}$
$S5=(2\cos x-1)(2\cos2x-1)...(2\cos2^{n-1}x-1)$
S6=$\frac{1}{\cos a+\cos a}$+$\frac{1}{\cos a+\cos3a}$+...$\frac{1}{\cos a+\cos(2n+1)a}$