Question

Zadanie drugie w załączniku prosze :)

Answer 1

An = (2n² - 7n)/(n +6)
a)
a₁ = (2 * 1² - 7 * 1)/(1 + 6) = (2 - 7)/7 = - 5/7
a₂ = (2 * 2² - 7 * 2)/(2 + 6) = (2 * 4 - 14)/8 = (8 - 14)/8 = - 6/8 = - 3/4
a₃ = (2 * 3² - 7 * 3)/(3 + 6) = (2 * 9 - 21)/9 = (18 - 21)/9 = - 3/9 = - 1/3
a₄ = (2 * 4² - 7 * 4)/(4 + 6) = (2 * 16 - 28)/10 = (32 - 28)/10 = 4/10 = 2/5
monotoniczność
a₂ - a₁ = - 5/7 - ( - 3/4) = - 5/7 + 3/4 = - 20/28 + 21/28 = 1/28
 a(n + 1) - an > 0 to ciąg jest rosnący
1/28 > 0