q_n =Π_(n=0) ^∞ cos((x/2^n ))
i) study the variation of q_n
ii)
show that cosx=((sin2x)/(2sinx)) , ∀x∈[0,(π/2)]
iii)
deduce that q_n =(1/2^(n+1) )×((sin2x)/(sin((x/2^n ))))
iv)lim_(n→∞) q_n =?
v)
solve cos((x/2))≥−(1/2)
hi, dears masters !
A = {au+bv, (a, b, u, v) ∈ Z^4 } with a ≠ b.
1. prove that A is ideal of Z.
2. let 𝛌Z = {𝛌n , n ∈ Z}.
prove that A has a smaller element 𝛌 strictly
positive such that A = 𝛌Z.
3. prove that 𝛌 = gcd(a,b).