Question

Fie n,p apartine N si x=(-1) la puterea n+1 × 1/2 + (-1) la puterea n × 1/3 +(-1) la puterea p × 1/6. Calculati x , daca a.n si p nr. pare b.n si p nr. impare

Answer 1

a) n-par => n+1=impar => (-1)^(n+1) = -1
(-1)^n = 1
p-par => (-1)^p = 1
=> x= -1/2 + 1/3 + 1/6
b) n-impar => n+1=par => (-1)^(n+1) = 1
(-1)^n= -1
p-impar => (-1)^p = -1
=> x= 1/2 - 1/3 - 1/6