1 ]
n
n
n
n
n
n
→∞


+
+
+
+
+
+
+




=
2
2
2
-
1
1
2 lim
[(1 1 1)
(2
4 (2 – 2) ]
2
→∞
+ +
+
+
+
+
+
144244
3
n
n terms
n
n
n
=
2
2
2
2
1
2
2 lim
[
(1
2 ( –1) ]
n
n
n
n
n2
→∞
+
+
+
+
=
1
4 (
1)
(2 –1)
2 lim
[
]
6
n
n
n
n
nn
n2
→∞
−
+
=
1
2 (
1) (2 –1)
2 lim
[
]
3
n
n
n
nn
n
→∞
−
+
=
2
1
1
2 lim [1
(1
) (2 –
)]
3
n
n
n
→∞
+
−
 = 
4
2 [1
]
3
+
 = 14
3
334
MATHEMATICS
Example 26 Evaluate 
2
0
xe dx
∫
as the limit of a sum