Page 153 - vol2

n
! n (2 ) n
3) L = lim 4) L = lim
+
+
+
2
2
n
n→ (1 1 )(1 2 )...(1 n 2 ) n→ (2 )!
 1 1 1  ! n
5) L = lim  + + ... 2  6) L = lim
+
n
n→  (2 ) 2 (2n + 1) 2 (2n n − 1)  n→ 3 n
 1 2 n 
6) L = lim  + + ...+ 
4
n→  n + 1 n + 2 n +  4 n
4
1 3 2 3 n 3
7) L = lim + + ...+
4
4
4
n→ n + 1 n + 2 n + n
 cos1 cos2 cosn 
8) L = lim  + + ...+ 
2
2
n→  n + 1 n + 2 n +  2 n
+
+
+
cos1 cos2 ... cos n
9) L = lim
n→ n 2
 1 1 1 
10) L = lim + + ...+ 
+
n→ 3  n 2 3 (n + 1) 2 3 (n n − 1) 2 
 
+
+
+
1! 2! ... n !
11) L = lim
n
n→ (2 )!
 1 1 1 
12) L = lim  + + ...+ 
p
n→  p n + 1 p n + 2 p n +  p n
p

2
13) L = lim  n + + 1+ n + n
2
n
n→
 1 1 1 
14) b = limn  1− − − ...− 
n
n→  p n + 1 p n + 2 p n +  p n
p
p
 n k 
15) L = lim  1+ − n 
n→   k= 1 n 2  

16) L = lim  n  2    n + + 1+ n + 1
2
2
n
n→ n
! n
17) L = lim
n→ (2 + 1)(2 + 2)...(2 + ) n
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