Let s 1
​
=1 and s n+1
​
= 3
1
​
(s n
​
+1) for n≥1. (a) Find s 2
​
,s 3
​
and s 4
​
. (b) Use induction to show s n
​
> 2
1
​
for all n. (c) Show (s n
​
) is a decreasing sequence. (d) Show lims n
​
exists and find lims n
​
.