Math Is Fun Forum
Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °
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#1 2006-10-25 22:58:59
- etotheipi
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- Registered: 2006-10-25
- Posts: 1
Sequence problem (mildly tough)
Hi,
I had a bit of trouble with this but halfway through posting it realised how to do it 
but thought id post it anyway for your fun... enjoy
For θ≤pi/2, find a formula for sin²(θ/2) as a function of sin²(θ). Hence show that the sequence defined by
a_1=1, a_n+1=0.5(1-√(1-a_n) [where a_n means "a subscript n"]
has the property that a_n=sin²(pi/2^n) for all n
enjoy 
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#2 2011-05-20 05:50:54
- gAr
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- Registered: 2011-01-09
- Posts: 3,482
Re: Sequence problem (mildly tough)
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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