Math Is Fun Forum

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