The first term of a progression is $$\(\sin ^{2} \theta\)$$, where $$\(0< \theta< \frac{1}{2} \pi\)$$. The second term of the progression is $$\(\sin ^{2} \theta \cos ^{2} \theta\)$$ Given that the progression is geometric, find the sum to infinity. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_s20_qp_13 Year：2020 Question No：8(a)
Answer:
\(r=\cos ^{2} \theta \quad\) SOI
\(S_{\infty}=\frac{\sin ^{2} \theta}{1-\cos ^{2} \theta}\)
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\(S_{\infty}=\frac{\sin ^{2} \theta}{1-\cos ^{2} \theta}\)
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Knowledge points:
1.6.3 use the formulae for the nth term and for the sum of the first n terms to solve problems involving arithmetic or geometric progressions (Including knowledge that numbers a,b,c are 'in arithmetic progression' if 2 b=a+c (or equivalent) and are 'in geometric progression' if (or equivalent) (Questions may involve more than one progression.)
1.6.4 use the condition for the convergence of a geometric progression, and the formula for the sum to infinity of a convergent geometric progression.
Solution:
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