Question

lim n стремится к бесконечности ((n+2)!+5n!)/2(n+2)!-n!

Answer 1

Ответ:

lim ((n+2)!+5n!)/(2(n+2)!-n!)

n-->∞

Упростим выражение

((n+2)!+5n!)/(2(n+2)!-n!)

n!((n+1)(n+2)+5)/n!(2(n+1)(n+2)-1)

((n+1)(n+2)+5)/(2(n+1)(n+2)-1)

(n²+3n+2+5)/(2(n²+3n+2)-1)

(n²+3n+7)/(2n²+6n+3)

lim ((n²+3n+7)/(2n²+6n+3))

n-->∞

lim ((1+3/n+7/n²)/(2+6/n+3/n²)=1/2

n-->∞