Question

(poza aici) Scrieti primii 5 termeni ai sirului (Xn)n>=1:
a) Xn=3n-2/n+2
b) Xn=1+(-1)la puterea n)/3

Answer 1

1a)

xn=(3n-2)/(n+2)

x₁=(3·1-2)/(1+2)=1/3

x₂=(3·2-2)/(2+2)=4/4=1

x₃=(3·3-2)/(3+2)=7/5

x₄=(3·4-2)/(4+2)=10/6=5/3

x₅=(3·5-2)/(5+2)=13/7

b)

xn=(1+(-1)ⁿ]/3=

x₁= (1 + (-1)⁰]/3 = (1 + 1)/3 = 2/3

x₂ = (1 + (-1)¹]/3 = (1 - 1)/3 = 0

x₃ = (1 + (-1)²] /3 =(1 + 1)/3 = 2/3

x₄ = (1 + (-1)³]/3 = ( 1 - 1)/3 = 0

x₅ = (1 + (-1)⁴]/3= ( 1+ 1)/3 = 2/3