1. Calcule los siguientes límites:
n
n
3 5 7 9 2n 1
a) lim 5 8 11 14 3n 2
2n 1 2 1 1 1
(2 )
3n 2 3 3(3n 2) 3 3n 2
nn
n
1 9 15 21 27 1
lim ( (2 ))
3 5 8 11 14 3n 2
n
n
1 9 15 21 27 1
lim ( (2 ))
3 5 8 11 14 3n 2
n
n
1 9 15 21 27 1
lim (2 )
3 5 8 11 14 3n 2
Es una indeterminacion
0
aplicamos el segundo criterio de Stolz:
n (n 1)
n
9 15 21 27 1
(2 )
15 8 11 14 3n 2
lim 9 15 21 27 1
3(2 )
5 8 11 14 3(n 1) 2
n (n 1)
n
1
(2 )
13n 2
lim 1
3(2 )
3(n 1) 2
n n n
1 6n 3
(2 ) ( )
1 1 1 (6n 3)(3n 1) 1
3n 2 3n 2
lim lim lim (1)
1 6n 3
3 3 3 (6n 3)(3n 2) 3
(2 ) ( )
3n 1 3n 1
n
n
3 5 7 9 2n 1 1
lim 5 8 11 14 3n 2 3