Question

lim [n2-n+1/n2-n-1]n(n-1)
n_#
# is infinity

Answer 1

Answer:

e²

Step-by-step explanation:

Lim    [n² - n + 1/n² - n - 1]ⁿ⁽ⁿ⁻¹⁾

n -->∝

= Lim    [ 1 + (n² - n + 1/n² - n - 1 ) - 1 ]ⁿ⁽ⁿ⁻¹⁾  (added and subtracted 1)

  n -->∝

= Lim    [ 1 + 2/n² - n - 1  ]ⁿ⁽ⁿ⁻¹⁾  

  n -->∝

= Lim    [ 1 + 2/n² - n - 1  ]ⁿ⁽ⁿ⁻¹⁾ ˣ ²⁽ⁿ²⁻ⁿ⁻¹⁾/²⁽ⁿ²⁻ⁿ⁻¹⁾ ( Multiplied and divided by2(n² -

  n -->∝                                                               n - 1) on the power)

= е ^  Lim       2n(n-1)/n² - n - 1

         n -->∝          

= e²