Question

ZADANIE W ZAŁĄCZNIKU, rozwiązania z obliczeniami.

Answer 1

a)

a n = (-1)^n * (n² + 1)

 

a5 = (-1)^5 * (5² + 1) = (-1) * (25 + 1) = (-1) * 26 = - 26

 

a (n + 1) = (-1)^(n + 1) * [ (n + 1)² + 1 ] = (-1)^n * (-1)^1 * (n² + 2n + 1 + 1) = (-1)^n * (-1) * (n² + 2n + 2) = - (-1)^n * (n² + 2n + 2)

 

a (2n) = (-1)^(2n) * [ (2n)² + 1 ] = 1^n * (4n² + 1) = 1 * (4n² + 1) = 4n² + 1

 

b)

a 8 = (-1)^8 * (8² + 1) = 1 * (64 + 1) = 1 * 65 = 65

 

a (n -2) = (-1)^(n - 2) * [ (n - 2)² + 1 ] = (-1)^n * (-1)^(-2) * (n² - 4n + 4 + 1) = (-1)^n * (n² - 4n + 5)

 

a (2n + 2) = (-1)^(2n + 2) * [ (2n + 2)² + 1 ] = (-1)^2n * (-1)^2 * (4n² + 8n + 4 + 1) = 1^n * 1 * (4n² + 8n + 5) = 1^n * (4n² + 8n + 5)