Question

Найдите предел последовательности x_n= (n^3- 1+(1-〖n)〗^3)/(3n^3 )=

Answer 1

$lim_{n to infty} x_n= lim_{n to infty} frac{n^3- 1+(1-n)^3}{3n^3} = lim_{n to infty} frac{n^3-1+1-3n+3n^2-n^3}{3n^3} = \ =lim_{n to infty} frac{n^2-n}{n^3} =lim_{n to infty} ( frac{n^2}{n^3} -frac{n}{n^3} )= lim_{n to infty} ( frac{1}{n} - frac{1}{n^2} )=0-0=0$