Find the limit if it exists^ lim 20 3 15 20 3 15 20 3 15
n  


2 n roots
Solution
Introduce a sequence
x1  20 3 15
, xn  20 3 15 20 3 15 20 3 15 for n  2, 3,


2 n roots
This sequence is
1. bounded from above:
3
3
3
3
xn  20 15 20 15 20 3 15  20 20 20 20 20 3 20 

 
2 n roots
2 n roots
 20 20 20 20  20

1 1
1
   
2 4
2
2n
2n
 20
1 1
1
    
2 4
 2
0.5
 2010.5  20.
2 n roots
2. non-decreasing:
3
3
xn 1  20 15 20 15 20 3 15   n xn ,


2( n 1) roots
where  n 

20 3 15

mn
 1 , as


20 3 15  1
Hence, the limit exists. Let it be
equation for A
3
3
.
A, A  0 .
One has the following
A  20 15 20 15 20 3 15  20 3 15 A
,
которое преобразуем к виду A6  203 15 A . The answer is given by the
15
non-zero root A   203 15 .