Question

$lim( {3}^{n} - {4}^{n} ) \\ n - > \infty$

Answer 1

lim (3ⁿ - 4ⁿ)
n → ∞
.
lim (3ⁿ - 4ⁿ)•(3ⁿ +4ⁿ)/(3ⁿ + 4ⁿ)
n →∞
.
lim (3²ⁿ + 12ⁿ - 12ⁿ - 4²ⁿ)/(3ⁿ + 4ⁿ)
n→∞
.
lim (3²ⁿ - 4²ⁿ)/(3ⁿ + 4ⁿ)
n→∞
.
lim ((3/4)²ⁿ - 1)/((3/16)ⁿ + (4/16)ⁿ)
n→∞
.
= ((3/4)^∞ - 1) / ((3/16)^∞ + (1/4)^∞)
= (0 -1) / (0 + 0)
= -1/0
= -∞