FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.89
Example 182:Evaluate : h
Lt^11 ....^1
→ ∞ 1 2n 2 2n n 2n
(^) + + +
(^) + + + (^)
Expression =h
Lt 1/n 1/n .... 1/n
→ ∞ 1/n 2n/n 2/n 2n/n n/n 2n/n
(^) + + +
(^) + + + (^)
= h
Lt^111 ...^1
→ ∞n 1/n 2 2/n 2 n/n 2
(^) + + +
(^) + + +
n^1
h r (^10)
Lt^11 dx
n r 2 x 2
n
= → ∞ (^) = + = (^) +
= log x 2 log 3 log 2 log .( − )^01 = e − e = e^32
SELF EXAMINATION QUESTIONS
Evaluate :
2 2 2 2
n^3
lim1 2 3 ... n
→ ∞ n
+ + + + [Ans. 1
3 ]
- n
lim 1 1 ...^1
→ ∞ n 1 n 2 n n
(^) + +
(^) + + + [Ans. log 2]
- n
lim^11 ...^1
→ ∞ n m n 2m n nm
(^) + + +
(^) + + + [Ans. m^1 log 1 m(+ )]
4.
m m m m
n m 1
lim 1 2 3 ... n.
→ ∞ n+
(^) + + + +
[Ans.
1
m 1+ ]
5. ( ) ( )
2 2
n^33
lim 1 n n ....^1
→ ∞ n n 1 n 2 8n
(^) + + + +
(^) + + [Ans.