Answer to Question #60661 in Real Analysis for esita

Question

a) Prove that the sequence } { n
a where 2 2
2
3
2
+
=
n
an
, converges to 0 . (3)
b) Find the following limit, if it exists:
3
3 3
0 1 cos
sin lim
x
x x
x→ −
(2)
c) Test the convergence of the following series. (5)
i) 2 2
+ 2 2
+ 2 2
+L
7 .8
6.5
5 .6
4.3
3 .4
2.1
ii) ∑
+ − −
n
n 1 n 1