Functions Question 320
Question: $ \underset{n\to \infty }{\mathop{\lim }},{ \frac{1}{n^{2}}+\frac{2}{n^{2}}+\frac{3}{n^{2}}+……+\frac{n}{n^{2}} } $ is
[SCRA 1996]
Options:
A) ½
B) 0
C) 1
D) $ \infty $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \underset{n\to \infty }{\mathop{\lim }}( \frac{1}{n^{2}}+\frac{2}{n^{2}}+\frac{3}{n^{2}}+…….+\frac{n}{n^{2}} ) $ $ =\underset{n\to \infty }{\mathop{\lim }},( \frac{1+2+3+……+n}{n^{2}} )=\underset{n\to \infty }{\mathop{\lim }}\frac{\frac{n}{2}(n+1)}{n^{2}} $ $ =\frac{1}{2}\underset{n\to \infty }{\mathop{\lim }},\frac{n+1}{n}=\frac{1}{2}\underset{n\to \infty }{\mathop{\lim }},1+\frac{1}{n}=\frac{1}{2} $
BETA
