let be the sequence (x_n )n ≥ 1
defined by x_1 = 1
x_(n+2) = 3x_(n+1) − x_n
∀n ∈ N
find L =lim_(n→∞) ((Σ_(k=0) ^0 (x_(2k+1) /(x_k + x_(k+1) ))))^(1/n) = ?
Two cups m and n contains the same
mass of water, m is at 25°c while n is
at the temperature of 102°c. If both cups
are placed in the same freezer
of internal temperature - 45°c. Which of
the content of m and n freezes first ?
Hence,
show that tₘ⁻ tₙ = - wc In(²¹/₁₀).
where tₘ and tₙ are the time taken for
m and n to freezes and w is the mass
of water and c is specific heat capacity
of water.
Une fonction P est dite quasi polynomiale s′il existe (pour k∈N ) k+1 fonction periodique(c_i )_(i∈[∣0;k∣]) de Z dans R
telles que P(n)=Σ_(k=1) ^n c_i (n)n^i
(1) Montrez que l′ensemble des fonction quasi polynomiale forme un R−ev(real space vector).
(2)Montrez que si P,Q:Z→R sont desfonction quasi polynomiale tel que P(n)=Q(n) ∀n∈N alors P=Q