Paper 4: Fundamentals of Business Mathematics & Statistic

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 ]

2. n
   lim 1 1 ...^1
   → ∞ n 1 n 2 n n

(^) + +
(^) + + + [Ans. log 2]

3. 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.

3

8 ].