if three persons selected at random
are stopped on a street,what is
the probability that
(i)all were born on a friday?
(ii)two were born on a friday and
the others on a thursday?
(iii)none was born on a friday
1) find the radius of convergence?for
Σ_(n=1) ^∞ (x^n /(n(n+1)(n+2))) and calculate its sum
2) find the value of Σ_(n=1) ^∞ (((−1)^n )/(n 2^n (n+1)(n+2)))
let S(x)=Σ_(n=0) ^∞ f_n (x) with f_n (x)= (((−1)^n )/(n!(x+n)))
x∈]0,+∞[
1) prove that S id defined .calculate S(1) and
prove that ∀x>0 xS(x) −S(x+1) =(1/e)
2) prove that S is C^∞ on R^(+∗)
3) prove that S(x) ∼ (1/x) (x→0^+ ) .
let f_n (x)= n^x e^(−nx) with x>0
1) study the simple and uniform convervence for
Σ f_n (x)
2) let S(x)= Σ_(n=1) ^∞ f_n (x).prove that
S(x) ∼ (1/x) ( x→0^+ )