Question

Va rog frumos!!! Este urgent!

Answer 1

Răspuns:

∑₀⁰⁰3(a/9)ⁿ=3∑(a/9)ⁿ

a)Seria e covergenta daca (a/9)ⁿ->0 adica a/9∈(-1,1)  adica a∈(-9,9)

Pt a=5 seria  este

3∑(5/9)ⁿ

b)Calculezi suma sirurilor partiale

Sn =(5/9)⁰+(5/9)¹+(5/9)²+...+(5/9)ⁿ

=1+(5/9)¹+(5/9)²+...+(5/9)ⁿ

Ai o proogresie   geo,metrica   de   ratie  5/9

Sn=(5/9)*[1-(5/9)ⁿ⁺₁]/(1-5/9)=

(5/9)[1-5/9)ⁿ⁺¹]/(4/9)=(5/4)[[1-(5/9)ⁿ⁺¹

Lim Sₙ=5/4=>

3∑(5/9)ⁿ=3*5/4=15/4

Explicație pas cu pas: