本题目来源于试卷: Trigonometric Functions，类别为 IB数学
[问答题]
The first three term.fihr /1zkf4hsps d ,ctd(0nbr/ik-hrj2o.(u of a geometric sequence are
$\sqrt{2} \cos x, \sin 2 x$, $2 \sqrt{2} \sin ^{2} x \cos x$,$-\frac{\pi}{2} \lt x\lt\frac{\pi}{2}$ .
1. Find the common ratio.
2. Find the set of values of x for which the geometric series below converges.
$\sqrt{2} \cos x+\sin 2 x+2 \sqrt{2} \sin ^{2} x \cos x+\cdots$
Consider $x=\arcsin \left(\frac{1}{2 \sqrt{2}}\right), 0 \lt x \lt \frac{\pi}{2}$ .
3. Show that the sum to infinity of this series is $\sqrt{7}$ .
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